the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

estimation and statistical analysis of exponential polynomial signals we derive and analyze a suboptimal algorithm for estimating the unknown parameters of an exponential polynomial signal eps model the eps model represents a signal as an exponent raised to a complex polynomial of time that is the phase and the logarithm of the amplitude are approximated as finite order polynomials of time

liouville type results of curvature operators of fuchsian convex surfaces abstract in this paper we deduce some liouville type results of curvature operators of fuchsian convex surfaces in minkowski space

parabolic monge ampere equations on riemannian manifolds on a compact riemannian manifold m g we consider the parabolic monge ampere equation t x t logdet g x hess x t detg x x t f x x 0 phiv 0 x here is a real parameter andf 0 m r are smooth functions we show existence of for all timestindependent of if 0 then t t converges exponentially towards a solution of the stationary problem ast in the special case 0 f 0 one has 0 and we determine the convergence rate t in thel2 norm more precisely

regularity of generalized solutions of monge ampere equations on etudie la regularite interieure des solutions generalisees convexes des equations de monge ampere de la forme detd 2 d f x u du dans ou est un domaine de r n f est une fonction positive suffisamment lisse sur r r n

efficient evaluation of 1 d and 2 d polynomials at equispaced points an extension to the two dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two dimensional polynomials efficiently over general periodic parallelograms the problem of getting the initial values required for other fast algorithms is treated in a general manner fast algorithms are presented for computing initial values in both cases of one and two dimensional polynomials it is observed that the two dimensional recursion is not always advantageous compared with taking the one dimensional recursion for each variable separately

on fast evaluation of bivariate polynomials at equispaced arguments the initial value problem arising in the recursive evaluation of a 2d polynomial at equispaced points is treated in detail the results facilitate efficient implementation of bose s recursive algorithm the computational complexity is compared with that involved in a direct computation and some general observations are made for an alternative scheme proposed by x nie and r unbehauen 1989

regularity of subelliptic monge ampere equations in dimension n 3 for k x 2m that can be written as a sum of squares of smooth functions we prove that a c2 convex solution u to a subelliptic monge ampere equation detd2u k x u du is itself smooth if the elementary n 1 st symmetric curvature kn 1 of u is positive the case m 2 uses an additional nondegeneracy condition on the sum of squares our proof uses the partial legendre transform calabi s identity for uij ij where is the square of the third order derivatives of u the campanato method xu and zuily use to obtain regularity for systems of sums of squares of hormander vector fields and our earlier work using guan s subelliptic methods

w2 1 e estimates for the monge ampere equation abstract we study strictly convex alexandrov solutions u of the real monge ampere equation det 2 u f where f is measurable positive and bounded away from 0 and under only these assumptions we prove interior w 2 1 e regularity of u

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

efficient evaluation of multivariate polynomials over multidimensional grids let p x 1 x 2 x n be a multivariate polynomial in n variables x 1 x 2 x n and suppose that p x 1 x 2 x n is of degree m i in x i i 1 2 n it is shown how p x 1 x 2 x n may be evaluated at x i x 0i n i i for n i 0 1 2 and i 1 2 n using not more than m 1 m 2 m n additions per point feasibility of reduction from this upper bound is demonstrated in the n 2 case

on axially symmetric solutions of fully nonlinear elliptic equations we show that in dimension 3 axial symmetric viscosity solutions of uniformly elliptic hessian equations are in fact the classical ones

hessian equations on exterior domain abstract in the paper we consider the hessian equation k d 2 u f x where f is a positive function outside a bounded domain of r n n 3 and f x 1 o x for some 2 at infinity using the perron s method we prove the existence and uniqueness for viscosity solutions of exterior dirichlet problem with prescribed asymptotic behavior at infinity there are examples to show that the result is optimal this is an extension of the theorems given by bao li li in 2 for f 1 and bao li zhang in 3 for k n

singular boundary value problems for the monge ampere equation abstract given a strictly convex smooth and bounded domain in r n we consider solving the monge ampere equation det d 2 u f x u for solutions in c c with zero boundary value where the nonlinearity f x t could be singular at t 0 we will show that under some fairly general assumptions on f the above dirichlet problem admits a negative convex solution in uniqueness of such solutions is then established for a wide class of nonlinearities f x t as a consequence of a comparison principle

the obstacle problem for hessian equations on riemannian manifolds abstract in this paper we consider the obstacle problem for a class of fully nonlinear equations on riemannian manifolds the c 1 1 regularity of the greatest viscosity solutions is established

on the mean oscillation of the hessian of solutions to the monge ampere equation we give interior a priori estimates for the mean oscillation of second derivatives of solutions to the monge ampere equation detd2u f x with zero boundary values where f x is a non dini continuous function if the modulus of continuity of f x is f r such that limr 0f r log 1 r 0 then d2uvmo

liouville property and regularity of a hessian quotient equation we are concerned with properties of convex solutions to the hessian quotient equation sn c d2 p 1 k n as our first main result we prove some regularity of strong solutions while the second states that for p 1 an entire convex solution with a quadratic growth bound must be a quadratic polynomial

bifurcation and admissible solutions for the hessian equation abstract we study the following eigenvalue problem of k hessian equation s k d 2 u k f u in b u 0 on b global bifurcation result is established for this problem as applications of the bifurcation result we determine the intervals of for the existence nonexistence uniqueness and multiplicity of radially symmetric k admissible solutions for this problem

lattice boltzmann simulation of steady non newtonian blood flow in a 3d generic stenosis case a lattice boltzmann simulation of blood flow using the carreau yasuda model to calculate the non newtonian viscosity is described in this paper the carreau yasuda model is implemented in the lattice boltzmann software by adjusting the shear dependent viscosity over the relaxation parameter which is locally computed each time step by applying the newton iteration within the flow solver a scheme to compare the non newtonian and newtonian flow effects is proposed finally a comparison has been made between non newtonian and newtonian flow in a 3d generic stenosis

continuity of optimal transport maps and convexity of injectivity domains on small deformations of 2 given a compact riemannian manifold we study the regularity of the optimal transport map between two probability measures with cost given by the squared riemannian distance our strategy is to define a new form of the so called ma trudinger wang condition and to show that this condition together with the strict convexity on the nonfocal domains implies the continuity of the optimal transport map moreover our new condition again combined with the strict convexity of the nonfocal domains allows us to prove that all injectivity domains are strictly convex too these results apply for instance on any small c4 deformation of the 2 sphere 2009 wiley periodicals inc

the local regularity for strong solutions of the hessian quotient equation abstract by means of the reilly formula and the alexandrov maximum principle we obtain the local c 1 1 estimates of the w 2 p strong solutions to the hessian quotient equations for p sufficiently large and then prove that these solutions are smooth there are counterexamples to show that the integral exponent p is optimal in some cases we modify partially the known result in the hessian case and extend the regularity result in the special lagrangian case to the hessian quotient case

stabilized stress velocity pressure finite element formulations of the navier stokes problem for fluids with non linear viscosity abstract the three field stress velocity pressure mixed formulation of the incompressible navier stokes problem can lead to two different types of numerical instabilities the first is associated with the incompressibility and loss of stability in the calculation of the stress field and the second with the dominant convection the first type of instabilities can be overcome by choosing an interpolation for the unknowns that satisfies the appropriate inf sup conditions whereas the dominant convection requires a stabilized formulation in any case this paper proposes two stabilized schemes of sub grid scale sgs type differing in the definition of the space of the sub grid scales and both allowing to use the same interpolation for the variables u p deviatoric stress velocity and pressure even in problems where the convection component is dominant and the velocity stress gradients are high another aspect considered in this work is the non linearity of the viscosity modeled with constitutive models of quasi newtonian type this paper includes a description of the proposed methods some of their implementation issues and a discussion about benefits and drawbacks of a three field formulation several numerical examples serve to justify our claims

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

a local regularity of the complex monge ampere equation we prove a local regularity and a corresponding a priori estimate for plurisubharmonic solutions of the nondegenerate complex monge ampere equation assumingthattheir w 2 p normisundercontrolforsome p n n 1 thiscondition isoptimal weuseinparticularsomemethodsdevelopedbytrudingerandanestimate for the complex monge ampere equation due to kooodziej

sur les equations de monge ampere in this paper we study the real monge arapere equations det d2u f x in 0 u convex in 0 u 0 on 0 and we introduce a new method for solving these equations which enables us to show the existence of regular solutions this method uses only p d e techniques and does not use any geometrical results furthermore it enables us to solve quasilinear monge ampere equations

singular solutions to special lagrangian equations with subcritical phases and minimal surface systems we construct singular solutions to special lagrangian equations with subcritical phases and minimal surface systems a priori estimate breaking families of smooth solutions are also produced correspondingly a priori estimates for special lagrangian equations with certain convexity are largely known by now

on the fast generation of equally spaced values of the gaussian function a exp at t this correspondence describes a very simple two term nonlinear recursion due to teager that can be used to efficiently generate a sequence of equally spaced values of the gaussian function a exp at t an extension of the method reduces the computation required to only two multiplications per point

continuity estimates for solutions to the prescribed curvature dirichlet problem on etudie des solutions au probleme de dirichlet pour l equation de courbure moyenne prescrite ainsi que pour des equations de weingarten plus generales on etablit des modules d estimation de continuite dependant seulement des valeurs limites

a relationship between the z transform and the fourier transform a relationship between the one sided z transform and the one sided discrete time fourier transform is discussed every discrete time function that can result from the sampling of a periodic continuous time function is considered to be periodic a simple general equation is presented and discussed

w2 1 regularity for solutions of the monge ampere equation in this paper we prove that a strictly convex alexandrov solution u of the monge ampere equation with right hand side bounded away from zero and infinity is w 2 1 mathrm loc this is obtained by showing higher integrability a priori estimates for d 2 u namely d 2 u llog k l for any k

the constraint equations of lovelock gravity theories a new σk yamabe problem this paper is devoted to the study of the constraint equations of the lovelock gravity theories in the case of a conformally flat time symmetric and space like manifold we show that the hamiltonian constraint equation becomes a generalisation of the k yamabe problem that is to say the prescription of a linear combination of the k curvatures of the manifold we search solutions in a conformal class for a compact manifold using the existing results on the k yamabe problem we describe some cases in which they can be extended to this new problem this requires to study the concavity of some polynomial we do it in two ways regarding the concavity of a root of this polynomial which is connected to algebraic properties of the polynomial and seeking analytically a concavifying function this gives several cases in which a conformal solution exists finally we show an implicit function theorem in the case of a manifold with negative scalar curvature and find a conformal solution when the lovelock theories are close to general relativity this paper is devoted to the study of the constraint equations of the lovelock gravity theories in the case of a conformally flat time symmetric and space like manifold we show that the hamiltonian constraint equation becomes a generalisation of the k yamabe problem that is to say the prescription of a linear combination of the k curvatures of the manifold we search solutions in a conformal class for a compact manifold using the existing results on the k yamabe problem we describe some cases in which they can be extended to this new problem this requires to study the concavity of some polynomial we do it in two ways regarding the concavity of a root of this polynomial which is connected to algebraic properties of the polynomial and seeking analytically a concavifying function this gives several cases in which a conformal solution exists finally we show an implicit function theorem in the case of a manifold with negative scalar curvature and find a conformal solution when the lovelock t

the dirichlet problem for the degenerate elliptic monge ampere equation abstract the existence and uniqueness of the global c 1 1 3 solution to the dirichlet problem for the degenerate elliptic monge ampere equation are proved under mild conditions and the application to the equation of the prescribed nonnegative gauss curvature is also given

nonsmooth solutions for a class of fully nonlinear pde s on lie groups abstract in this paper we prove the existence of nonsmooth viscosity solutions for dirichlet problems involving a class a fully non linear operators on lie groups in particular we consider the elementary symmetric functions of the eigenvalues of the hessian built with left invariant vector fields

lattice boltzmann simulations of blood flow non newtonian rheology and clotting processes the numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent in this paper we consider a lattice boltzmann lb approach to bloodflow modeling and we implement a non newtonian correction in order to reproduce more realistic flow profiles we obtain a good agreement between simulations and casson s model of blood rheology in a simple geometry finally we discuss how by using a passive scalar suspension model with aggregation on top of the lb dynamics we can describe the clotting processes in the aneurysm

existence of multiple solutions to the equations of monge ampere type abstract in this paper we prove the existence of nontrivial convex solutions to the monge ampere equation det d 2 u x u du with dirichlet or neumann boundary condition where x 0 0 0 we also deal with the existence and multiplicity of convex solutions to the equation det d 2 u x u du our results show that the existence of convex solutions of monge ampere equations is analogous to that of positive solutions of semilinear elliptic equations

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

the neumann problem for equations of monge ampere type we prove the existence of a classical solution to a neumann type problem for nonlinear elliptic equations of monge ampere type the methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed gauss curvature we also present applications to asymptotic problems which approach the non unique case and maximum principles for linear equations of aleksandrov bakelman type

a note on efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments by a h nuttall a h nuttall s see ibid vol assp 35 no 10 p 1486 7 1987 algorithm for the evaluation of a polynomial at a large number of arguments is addressed the authors supplement nuttall s treatment of the problem by 1 giving a relationship between the coefficients of the original polynomial and those of the equivalent one in terms of the integer variable n and 2 by deriving a formula for the computation of the initial values required for nuttall s recursive procedure to commence as a result of these supplements the recursive algorithm is completely programmable and can be efficiently implemented for any order n of the polynomial some general observations are made on the computational complexity in recursive evaluation in contrast to direct evaluation of a polynomial

transverse fully nonlinear equations on sasakian manifolds and applications abstract we prove a priori estimates for a class of transverse fully nonlinear equations on sasakian manifolds and give some geometric applications such as the transversion calabi yau theorem for transverse balanced and strongly gauduchon metrics we also explain that similar results hold on compact oriented taut transverse hermitian foliated manifold of complex co dimension n and give some geometric applications such as the transverse calabi yau theorems for transverse hermitian and strongly gauduchon metrics