root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

fine level set structure of flat isometric immersions a result by pogorelov asserts that c 1 isometric immersions u of a bounded domain s subset mathbb r 2 into mathbb r 3 whose normal takes values in a set of zero area enjoy the following regularity property the gradient f nabla u is developable in the sense that the nondegenerate level sets of f consist of straight line segments intersecting the boundary of s at both endpoints motivated by applications in nonlinear elasticity we study the level set structure of such f when s is an arbitrary bounded lipschitz domain we show that f can be approximated by uniformly bounded maps with a simplified level set structure we also show that the domain s can be decomposed up to a controlled remainder into finitely many subdomains each of which admits a global line of curvature parametrization

holder continuity of parabolic quasi minimizers abstract we are concerned with scalar valued local parabolic quasi minimizers u associated to a caratheodory integrand f obeying p growth assumptions for p 1 for such parabolic quasi minimizers we prove local holder continuity provided they are already locally bounded the superquadratic case p 2 has already been considered in 17 22 whereas the subquadratic case could at least to our knowledge not be treated in the past in this paper we are able to handle both the sub and superquadratic case under more general growth conditions

the regularity for nonlinear parabolic systems of p laplacian type with critical growth abstract we study the holder regularity of weak solutions to the evolutionary p laplacian system with critical growth on the gradient we establish a natural criterion for proving that a small solution and its gradient are locally holder continuous almost everywhere actually our regularity result recovers the classical result in the case p 2 16 and can be applied to study the regularity of the heat flow for m dimensional h systems as well as the m harmonic flow

very weak solutions of degenerate parabolic systems with non standard p x t growth abstract we study higher integrability of very weak solutions to certain degenerate parabolic systems whose model is the parabolic p x t laplacian system t u div d u p x t 2 d u div f p x t 2 f under natural assumptions on the exponent function p 0 t 2 we prove that any very weak solution u 0 t r n with d u p 1 e l 1 belongs to the natural energy space i e d u p l loc 1 provided e 0 is small enough

approximation of flat w2 2 isometric immersions by smooth ones let s subset mathbb r 2 be a bounded lipschitz domain and denote by w 2 2 text iso s mathbb r 3 the set of mappings u in w 2 2 s mathbb r 3 which satisfy nabla u t nabla u id almost everywhere under an additional regularity condition on the boundary partial s which is satisfied if partial s is piecewise continuously differentiable we prove that the strong w2 2 closure of w 2 2 text iso s mathbb r 3 cap c infty overline s mathbb r 3 agrees with w 2 2 text iso s mathbb r 3

efficient estimation and inferences for varying coefficient models abstract this article deals with statistical inferences based on the varying coefficient models proposed by hastie and tibshirani local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established the standard error formulas for estimated coefficients are derived and are empirically tested a goodness of fit test technique based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying coefficient model are constant or whether any covariates are statistically significant in the model the null distribution of the test is estimated by a conditional bootstrap method our estimation techniques involve solving hundreds of local likelihood equations to reduce the computational burden a one step newton raphson estimator is proposed and implemented the resulting one step procedure is shown to save computational cost on an order of tens with no

second order analysis for thin structures the eective behavior of second order strain energy densities is obtained using relaxation and i convergence techniques the cosserat theory see e g 13 14 and 2 is recovered within a dimension reduction analysis for 3d non linear elastic thin domains with varying profiles homogeneous and inhomogeneous plate models with periodic profiles are treated

remarks on holder continuity for solutions of the p laplace evolution equations we study the interior holder regularity problem for the gradient of solutions of the p laplace evolution equations with the external forces misawa gave some conditions for the holder continuity of the gradient of solutions we show holder estimates of the solutions with weaker condition as for misawa

functional coefficient instrumental variables models we consider estimation of nonparametric structural models under a functional coefficient representation for the regression function under this representation models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables a nonparametric generalization of random coefficient models the functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed and partially linear models over which they have appreciable flexibility we propose two step estimators that use local linear approximations in both steps the first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors our large sample results include consistency and asymptotic normality of the proposed estimators the high practical power of estimators is illustrated via both a monte carlo simulation study and an application to returns to education

on the justification of the nonlinear inextensional plate model we consider a cylindrical three dimensional body made of a saint venant kirchhoff material and we let its thickness go to zero for a specific order of magnitude for the applied loads and under appropriate restrictions on the set of admissible deformations we show that the almost minimizers of the total energy converge toward deformations that minimize the nonlinear bending energy obtained by fox raoult and simo using formal asymptotic expansions our result is obtained by convergence arguments

regularity results for nonlinear parabolic obstacle problems with subquadratic growth abstract in 26 it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local holder continuous provided the obstacle is regular enough in this paper we extend this regularity result to the subquadratic case this means we establish the local holder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth more precisely we prove that d u c loc 0 2 for some 0 1 provided the coefficients and the obstacle are regular enough moreover we use the local holder continuity to prove the local lipschitz continuity of the solution u i e u c loc 0 1 1 2

stability of slender bodies under compression and validity of the von karman theory since their formulation almost 100 years ago the von karman vk plate equations have been frequently used both by engineers and by analysts to study thin elastic bodies in particular their stability behaviour under applied loads at the same time the derivation of these equations met some harsh criticism and their precise mathematical status has been unclear until very recently following up on a recent variational derivation of the vk theory by friesecke james and muller from three dimensional nonlinear elasticity we study the predictions and the validity of the vk equation in the presence of in plane compressive forces the first main result is a stability alternative either the load leads to instability already in the nonlinear bending theory of plates kirchhoff love theory or it leads to an instability in a geometrically linear kl theory linearized instability or vk theory is valid the second main result states that under suitable conditions the critical loads for nonlinear stability and linearized instability coincide the third main result asserts this critical load also agrees with the load beyond which the infimum of the vk functional is the main ingredients are a sharp rigidity estimate for maps with low elastic energy and a study of the properties of isometric immersions from a set in mathbb r 2 to mathbb r 3 and their geometrically linear counterparts

asymptotic analysis of linearly elastic shells iii justification of koiter s shell equations we consider as in part i a family of linearly elastic shells of thickness 2 all having the same middle surfaces r3 where r2 is a bounded and connected open set with a lipschitz continuous boundary and l3 r3 the shells are clamped on a portion of their lateral face whose middle line is 0 where 0 is any portion of withlength 0 0 we make an essential geometrical assumption on the middle surfaces and on the set 0 which states that the space of inextensional displacements begin gathered v f omega eta eta i in h 1 omega times h 1 omega times h 2 omega hfill eta i partial v eta 3 0 on gamma 0 gamma alpha beta eta 0 in omega hfill end gathered where gamma alpha beta are the components of the linearized change is metric tensor ofs contains non zero functions this assumption is satisfied in particular ifs is a portion of cylinder and 0 is contained in a generatrix ofs

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

boundedness of the gradient for a doubly nonlinear parabolic equation we prove the local boundedness of the gradient for positive solutions to a doubly nonlinear parabolic equation in the case when the standard lebesgue measure has been replaced by a doubling measure which supports a weak poincare inequality

partial regularity for subquadratic parabolic systems under controllable growth conditions in this paper we prove a regularity result for weak solutions away from singular set of parabolic systems with subquadratic growth condition of the type tu z diva z u du b z u du for z x t where the structure function a satisfies standard ellipticity and growth condition with polynomial growth rate 2nn 2 p 2 the inhomogeneity b satisfies the controllable growth condition b z u du 1 u p 1 du p 1 1p where p n 2 pn 2 p if n 2 p here p can be any exponent if n 2 p the proof is based on the a caloric approximation lemma to parabolic systems with subquadratic growth

on the cauchy problem for the fast diffusion equation abstract for u 0 1 u 0 l loc 1 r n the author studies the existence of a kind of weak solution to the cauchy problem u t div u m 1 d u in r n 0 t u x 0 u 0 x 0 in r n where m 0 is a constant the uniqueness and regularity of solutions are also discussed

a semiparametric quantile panel data model with an application to estimating the growth effect of fdi abstract this paper estimates the impact of foreign direct investment on economic growth by proposing a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant a three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated a simple and easily implemented procedure for making inferences is proposed monte carlo simulation is conducted to examine the finite sample performance of the proposed estimators finally using the cross country panel data we find a strong empirical evidence of the existence of the absorptive capacity hypothesis together with another new finding that fdi has much stronger growth effects for countries with fast economic growth than for those with slow economic growth

regularity properties of isometric immersions we show that an isometric immersion y from a two dimensional domain s with c1 boundary to 3 which belongs to the critical sobolev space w2 2 is c1 up to the boundary more generally c1 regularity up to the boundary holds for all scalar functions v w2 2 s which satisfy det 2v 0 if s has only lipschitz boundary we show such v can be approximated in w2 2 by functions vk w1 w2 2 with det 2vk 0

functional coefficient autoregressive models in this article we propose a new class of models for nonlinear time series analysis investigate properties of the proposed model and suggest a modeling procedure for building such a model the proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics a consistency result is given to support the procedure for illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially improve postsample multi step ahead forecasts over other models

derivation of von karman plate theory in the framework of three dimensional viscoelasticity we apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite strain setting in kelvin s voigt s rheology to derive a viscoelastic plate model of von karman type we start from time discrete solutions to a model of three dimensional viscoelasticity considered in friedrich and kru ik siam j math anal 50 4426 4456 2018 where the viscosity stress tensor complies with the principle of time continuous frame indifference combining the derivation of nonlinear plate theory by friesecke james and muller commun pure appl math 55 1461 1506 2002 arch ration mech anal 180 183 236 2006 and the abstract theory of gradient flows in metric spaces by sandier and serfaty commun pure appl math 57 1627 1672 2004 we perform a dimension reduction from three dimensions to two dimensions and identify weak solutions of viscoelastic form of von karman plates

modeling and testing smooth structural changes with endogenous regressors abstract modeling and detecting parameter stability of econometric models is a long standing problem most existing estimation and testing methods are designed for models without endogeneity little attention has been paid to models with endogeneous regressors which may arise in many scenarios in economics in this paper we first consider a time varying coefficient time series model with potential time varying endogeneity a local linear two stage least squared estimation is developed to estimate coefficient functions the consistency and asymptotic normality of the estimator are derived furthermore a nonparametric test is proposed to check smooth structural changes as well as abrupt structural breaks with possibly unknown change points in regression models with potential endogeneity the idea is to compare the fitted values of the unrestricted nonparametric time varying coefficient model and the restricted constant parameter model the test has an asymptotic n 0 1 distribution and does not require any prior information about the alternatives a simulation study highlights the merits of the proposed estimator and test in an application we estimate the new keynesian phillips curve for the us nonparametrically and find strong evidence against its stability

existence of weak solutions of doubly nonlinear parabolic equations abstract we deal with a cauchy dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space time cylinder for doubly nonlinear parabolic equations whose prototype is t u div u m 1 d u p 2 d u f with a non negative lebesgue function f on the right hand side where p 2 n n 2 and m 0 the central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f the constructed solution is obtained by a limit of approximations i e we use solutions of regularized cauchy dirichlet problems and pass to the limit to receive a solution for the original cauchy dirichlet problem

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

regularity for parabolic systems of uhlenbeck type with orlicz growth abstract we study the local regularity of p caloric functions or more generally of caloric functions in particular we study local solutions of non linear parabolic systems with homogeneous right hand side where the leading terms have uhlenbeck structure of orlicz type this paper closes the gap of 23 where liebermann proved that if the gradient of a solution is bounded it is holder continuous the crucial step is a novel local estimates for the gradient of the solutions which generalize and improve the pioneering estimates of dibenedetto and friedman 12 10 for the p laplace heat equation

gradient estimates for solutions of parabolic equations and systems 1 statement of the problem let 52 c r n 2 be a bounded domain with smooth boundary r 2 in this note we study scalar quasilinear parabolic differential equations u div y g ivul vu f u 0 1 u a u f u o 2 and systems u da u f u 0 3 on q x 0 co with initial conditions u 0 u0 resp u 0 u0 and homogeneous dirichlet boundary conditions u i x o co o for 1 and 2 resp 4 u1r x 0 00 0 for 3 5

a framework for nonlinear shells based on generalized stress and strain measures a very general class of shell theories is established based on a unified variational principle and on expansions with respect to biorthogonal function systems the shell models derived are able to accommodate the flow theory of large strain thermoelastoplasticity including the effects due to unloading the specific case of a compressible neo hookean material with a von mises yield condition is discussed in detail

invertibility and non invertibility in thin elastic structures the nonlinear elastic energy of a thin film of thickness h is given by a functional eh friesecke james and muller derived the limits as h 0 of the functionals h eh for 3 in this article we study the invertibility properties of almost minimizers of these functionals and more generally of sequences with equiintegrable energy density we show that they are invertible almost everywhere away from a thin boundary layer near the film surface moreover we obtain an upper bound for the width of this layer and a uniform upper bound on the diameter of preimages we construct examples showing that these bounds are sharp in particular for all 3 there exist lipschitz continuous low energy deformations which are not locally invertible

sieve instrumental variable quantile regression estimation of functional coefficient models abstract in this paper we consider sieve instrumental variable quantile regression ivqr estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates we estimate the functional coefficients by the sieve ivqr technique and establish the uniform consistency and asymptotic normality of the estimators based on the sieve estimates we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic we conduct simulations to evaluate the finite sample behavior of our estimator and test statistic and apply our method to study the estimation of quantile engel curves

korn type inequalities in orlicz spaces abstract we exhibit balance conditions between a young function a and a young function b for a korn type inequality to hold between the l b norm of the gradient of vector valued functions and the l a norm of its symmetric part in particular we extend a standard form of the korn inequality in l p with 1 p and an orlicz version involving a young function a satisfying both the 2 and the 2 condition

the intricate global structure of buckled states of compressible columns singularity theory and global multiparameter bifurcation theory are combined to show that nonbifurcating buckled states of compressible nonlinearly elastic columns lie on branches having detailed qualitative properties these properties distinguish the branches globally together with a delicate asymptotic analysis they are used to show that the global disposition of solution branches both bifurcating and not is strikingly different from that for incompressible columns

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

justification of the nonlinear kirchhoff love theory of plates as the application of a new singular inverse method in the framework of isotropic homogeneous nonlinear elasticity for a st venant kirchhoff material we consider a three dimensional plate of thickness and periodic in the two other directions using a new method that we call the singular inverse method we prove the existence of a solution rescaled uniformly in for small forces and at the same time we prove the rigorous convergence of this rescaled solution to the solution of the nonlinear kirchhoff love plate model we also state a 3d 2d error estimate

an invariant infinitesimal theory of motions superposed on a given motion abstract the development is applicable to any material but special attention is given to elastic solids included as a special case is an infinitesimal theory of elasticity with the following properties 1 it is properly invariant under arbitrary not necessarily infinitesimal superposed rigid body motions 2 it reduces by specialization to the theory of rigid bodies undergoing finite motion and 3 it can be brought into correspondence with the classical linear elasticity through a suitable reinterpretation of the symbols in the constitutive equation of the latter author

geometrically nonlinear flexural vibrations of plates in plane boundary conditions and some symmetry properties abstract this study is devoted to the derivation of some properties of the von karman equations for geometrically nonlinear models of plates with a boundary of arbitrary shape for applications to nonlinear vibration and buckling an intrinsic formulation of the local partial differential equations in terms of the transverse displacement and an airy stress function as unknowns is provided classical homogeneous boundary conditions with vanishing prescribed forces and displacements are derived in terms of the airy stress function in the case of a boundary of arbitrary geometry a special property of this operator crucial for some energy conserving numerical schemes and called triple self adjointness is derived in the case of an edge of arbitrary shape it is shown that this property takes a simple form for some classical boundary conditions so that the calculations in some practical cases are also simplified the applications of this work are either semi analytical methods of solution using an expansion of the solution onto an eigenmode basis of the associated linear problem or special energy conserving numerical methods

the role of non linear theories in transient dynamic analysis of flexible structures abstract transient dynamic analysis of flexible structures undergoing large motions is considered for rotating structures it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non linear at least second order beam theory use of a first order linearized linear beam theory results in a spurious loss of bending stiffness for a rotating plane beam a set of linear partial differential equations of motion that includes all inertia effects coriolis centrifugal acceleration of revolution and coupling between extensional and flexural deformations is derived from the fully non linear beam theory by consistent linearization the analysis is subsequently extended to the more general case of a plate accomodating shear deformation and undergoing a general three dimensional rotating motion the discretization process of the resulting linear equations of motion for the beam and the plate is also discussed

new integral estimates for deformations in terms of their nonlinear strains if u is a bi lipschitzian deformation of a bounded lipschitz domain in ln n 2 we show that the lp norm p 1 p n of a certain nonlinear strain function e u associated with u dominates the distance in lq q np n p if p n from u to a suitably chosen rigid motion of n this work extends that of f john who proved corresponding estimates for p 1 under the hypothesis that u has uniformly small strain we also obtain a bound for the oscillation of du in l2 these estimates are apparently the first to apply with no a priori pointwise hypotheses upon the strain of u in 3 the integral int limits omega e u 2d 3 is dominated by typical hyperelastic energy functionals proposed in the literature for modeling the behavior of rubber thus the case n 3 p 2 gives the first general bound for the deformations of such materials in terms of the associated nonlinear elastic work

local holder continuity of weak solutions to a diffusive shallow medium equation abstract we show the local holder continuity of bounded weak solutions to a doubly nonlinear parabolic equation used in models for diffusion of shallow media

variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results we use a variational convergence method to study the consistency of various cosserat hypotheses in shell theory with the limit nonlinear membrane model derived from three dimensional elasticity in the course of the analysis we introduce a generalization of quasiconvexity that is suitable for problems of the calculus of variations with two vectorial unknowns one of which appears through its gradient the other one through its value in a weak w 1 p l p framework

holder estimates for parabolic p x t laplacian systems in this paper we establish the local holder continuity of the spatial gradient of weak solutions to the parabolic p x t laplacian system begin array lll partial t u rm div left a x t du p x t 2 du right 0 end array more precisely we prove that begin array lll du in c rm loc 0 alpha alpha 2 quad rm for some alpha in 0 1 end array provided p and a are holder continuous

on sign changing and multiple solutions of the p laplacian abstract in this paper we construct the pseudo gradient vector field in w 0 1 p by which we obtain the positive and negative cones of w 0 1 p are both invariant sets of the descent flow of the corresponding functional then we use differential equations theory in banach spaces and dynamics theory to study p laplacian boundary value problems with jumping nonlinearities at zero or infinity and get new multiple solutions and sign changing solutions theorems of p laplacian

varying coefficient panel data model in the presence of endogenous selectivity and fixed effects this paper considers a exible panel data sample selection model in which i the outcome equation is permitted to take a semiparametric varying coecient form to capture potential parameter heterogeneity in the relationship of interest ii both the outcome and parametric selection equations contain unobserved xed eects and iii selection is generalized to a polychotomous case we propose a two stage estimator given consistent parameter estimates from the selection equation obtained in the rst stage we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time the selection bias term is then asymptotically removed from the equation along with xed eects using kernel based weights the proposed estimator is consistent and asymptotically normal we rst investigate the nite sample properties of the estimator in a small monte carlo study and then apply it to study production technologies of u s retail credit unions from 2002 to 2006

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

dynamical poroplasticity model with mixed boundary conditions theory for lm type nonlinearity we investigate the existence theory to the non coercive fully dynamic model of poroplasticity with nonhomogeneous mixed boundary condition and constitutive equation which belongs to the class lm existence of the solution to this model is proved by using the coercive and yosida approximations under the lowest possible assumptions about lm type nonlinearity of non gradient type under higher assumptions about the constitutive equation and boundary conditions see section 7 we obtain uniqueness and higher regularity of the solutions

stabilization of solutions for a class of degenerate equations in divergence form in one space dimension abstract by extending the concept of the liapunov functional and an idea due to dafermos we establish an invariance principle for a class of not necessarily strongly monotone systems this principle is then applied to continuous contraction strongly monotone systems on a hubert space and to a class of l 1 contraction monotone semigroups generated by degenerate equations in divergence form in one space dimension

instrumental variables estimators of nonparametric models with discrete endogenous regressors this paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor a two step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two stage least squares linear functionals of the model are shown to be asymptotically normal and a consistent estimator of the asymptotic covariance matrix is described for the binary endogenous regressor case it is shown that one functional of the model is a conditional on covariates local average treatment effect that permits both unobservable and observable heterogeneity in treatments finite sample properties of the estimators from a monte carlo simulation study illustrate the practicability of the proposed estimators

a quantitative modulus of continuity for the two phase stefan problem we derive the quantitative modulus of continuity omega r left p ln left frac r 0 r right right alpha n p which we conjecture to be optimal for solutions of the p degenerate two phase stefan problem even in the classical case p 2 this represents a twofold improvement with respect to the early 1980 s state of the art results by caffarelli evans arch rational mech anal 81 3 199 220 1983 and dibenedetto ann mat pura appl 103 4 131 176 1982 in the sense that we discard one logarithm iteration and obtain an explicit value for the exponent n p

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

a justification of nonlinear properly invariant plate theories a single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame invariance properties of three dimensional finite elasticity by a successive scaling of the external loading on the three dimensional body the nonlinear membrane theory the nonlinear inextensional theory and the von karman equations are derived as the leading order terms in the asymptotic expansion of finite elasticity the governing equations of the nonlinear inextensional theory are of particular interest where 1 plane strain kinematics and plane stress constitutive equations are derived simultaneously from the asymptotic analysis 2 the theory can be phrased as a minimization problem over the space of isometric deformations of a surface and 3 the local equilibrium equations are identical to those arising in the one director cosserat shell model furthermore it can be concluded that with a regular single scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading order term of an asymptotic analysis

regularity of solutions of nonlinear degenerate parabolic systems soit le systeme parabolique u i t div u p 2 u i 0 i m avec p 1 ou u i u i x t grad x et x r n ouvert pour toute solution de ce systeme avec max 1 2n n 2 p u est continu dans t

contractive properties for the heat equation in sobolev spaces abstract consider the heat equation r u x u 0 in a cylinder 0 t r n 1 smooth lateral boundary under zero neumann or dirichlet conditions geometric conditions for are given that guarantee that for a given p x u t l p will be non increasing for any solution decay rates are also given for arbitrary and p it is shown how to construct an equivalent l p norm such that x t is non increasing in this norm

nonlinearly elastic shell models a formal asymptotic approach ii the flexural model this paper is the sequel of part i in which the limiting displacement field of a thin shell when its thickness approaches zero is identified as the solution of a two dimensional nonlinear membrane shell model when the geometry of the middle surface of the shell and the boundary conditions allow non zero inextensional displacements the previous membrane limit model is not relevant in this case we show how to update the assumptions on the applied forces acting on the shell so that a limiting model can be derived by an asymptotic analysis furthermore we identify this limit as the two dimensional nonlinear flexural shell model

identification and sequential estimation of panel data models with insufficient exclusion restrictions abstract this paper presents estimators for nonparametric panel data models with additive fixed effects we analyze a model in which the entire regressor vector consisting of time varying as well as time invariant regressors is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model it is shown that when the model satisfies the additive interactive regression air representation of andrews and whang economic theory 6 1990 466 480 a sequential estimator consistently estimates the model the limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal finite sample properties of the estimator are considered in a monte carlo simulation study and used to estimate the returns to education in a cohort of mature men from the national longitudinal survey

l a priori bounds for gradients of solutions to quasilinear inhomogeneous fast growing parabolic systems abstract we prove boundedness of gradients of solutions to quasilinear parabolic systems the main part of which is a generalization to the p laplacian and its right hand side s growth depending on the gradient is not slower and generally strictly faster than p 1 this result may be seen as a generalization to the classical notion of a controllable growth of the right hand side introduced by campanato over gradients of p laplacian like systems energy estimates and a nonlinear iteration procedure of the moser type are cornerstones of the used method

functional coefficient regression models for nonlinear time series abstract the local linear regression technique is applied to estimation of functional coefficient regression models for time series data the models include threshold autoregressive models and functional coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross validatory estimation for the expected forecasting errors the proposed methodology is data analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality the asymptotic properties of the proposed estimators are investigated under the mixing condition both simulated and real data examples are used for illustration

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

regularity in parabolic systems with continuous coefficients under the only assumption of continuous coefficients we prove a partial holder continuity result for solutions to parabolic systems with polynomial growth a key component throughout the argument is the use of dibenedetto s intrinsic geometry degenerate parabolic equations universitext springer new york 1993 to accommodate the inhomogeneity in the system a main technical point is that although we are proving the holder continuity of solutions we employ the intrinsic geometry using cylinder stretched according to the size of the spatial gradient in an iteration scheme that does not necessarily imply the boundedness of the gradient itself

a boundary modulus of continuity for a class of singular parabolic equations abstract parabolic equations describing diffusion phenomena with change of phase are considered it is demonstrated that weak solutions are continuous up to the parabolic boundary of the domain of definition the continuity is quantitatively described by a modulus determined a priori only in terms of the data

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size