existence for coupled pseudomonotone strongly monotone systems and application to a cahn hilliard model with elasticity abstract a system of two operator equations is considered one of pseudomonotone type and the other of strongly monotone type both being strongly coupled conditions are given that allow to reduce the solvability of this system to a single operator equation of a pseudomonotone mapping this result is applied to a coupled system consisting of a parabolic equation of fourth order in space of cahn hilliard type and a nonlinear elliptic equation of second order modeling a quasi steady mechanical equilibrium using an appropriate notion of weak solutions and a framework for evolution equations developed by groger 2001 the system is reduced to a single parabolic operator equation and the existence of solutions is shown under restrictions on the strength of the coupling

the mixed problem in lipschitz domains with general decompositions of the boundary this paper continues the study of the mixed problem for the laplacian we consider a bounded lipschitz domain rn n 2 with boundary that is decomposed as d n d and n disjoint we let denote the boundary of d relative to and impose conditions on the dimension and shape of and the sets n and d under these geometric criteria we show that there exists p0 1 depending on the domain such that for p in the interval 1 p0 the mixed problem with neumann data in the space lp n and dirichlet data in the sobolev space w 1 p d has a unique solution with the non tangential maximal function of the gradient of the solution in lp we also obtain results for p 1 when the dirichlet and neumann data comes from hardy spaces and a result when the boundary data comes from weighted sobolev spaces

maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

direction and stability of bifurcating solutions for a signorini problem abstract the equation u u g u u 0 is considered in a bounded domain in r 2 with a signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary it is assumed that g 0 0 for r is a bifurcation parameter a given eigenvalue of the linearized equation with the same boundary conditions is considered a smooth local bifurcation branch of non trivial solutions emanating at 0 from trivial solutions is studied we show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u 0 in the case when 0 is the first eigenvalue and the branch goes to the right we show that the bifurcating solutions are asymptotically stable in w 1 2 norm the stability of the trivial solution is also studied and an exchange of stability is obtained

optimal holder regularity for mixed boundary value problems abstract we continue our study of mixed boundary value problems lu 1 in mu 2 on u 3 on for second order elliptic operators l and first order oblique operators m a best possible estimate of the regularity of u is proved under weak hypotheses on the coefficients of l and m

regularity of the maxwell equations in heterogeneous media and lipschitz domains abstract this note establishes regularity estimates for the solution of the maxwell equations in lipschitz domains with non smooth coefficients and minimal regularity assumptions the argumentation relies on elliptic regularity estimates for the poisson problem with non smooth coefficients

an h s p text curl varomega estimate for the maxwell system we derive an h 0 s p text curl varomega estimate for the solutions of the maxwell type equations modeled with anisotropic and w s infty varomega regular coefficients here we obtain the regularity of the solutions for the integrability and smoothness indices p s in a plane domain characterized by the apriori lower upper bounds of a and the apriori upper bound of its holder semi norm of order s the proof relies on a perturbation argument generalizing groger s l p type estimate known for the elliptic problems to the maxwell system

extending sobolev functions with partially vanishing traces from locally e δ domains and applications to mixed boundary problems we prove that given any k n for each open set rn and any closed subset d of such that is locally an e domain near d there exists a linear and bounded extension operator ek d mapping for each p 1 the space wdk p into wdk p rn here with o denoting either or rn the space wdk p o is defined as the completion in the classical sobolev space wk p o of restrictions to o of functions from cc rn whose supports are disjoint from d in turn this result is used to develop a functional analytic theory for the class wdk p including intrinsic characterizations boundary traces and extensions results interpolation theorems among other things which is then employed in the treatment of mixed boundary value problems formulated in locally e domains finally we also prove extension results on the scales of besov and bessel potential spaces on e domains with partially vanishing traces on ahlfors regular sets and explore some of the implications of such extension results

differentiability of implicit functions beyond the implicit function theorem abstract the implicit function theorem ift can be used to deduce the differentiability of an implicit mapping s u y given by the equation e y u 0 however the ift is not applicable when different norms are necessary for the differentiation of e w r t y and the invertibility of the partial derivative e y y u we prove theorems ensuring the twice differentiability of the mapping s which can be applied in this case we highlight the application of our results to quasilinear partial differential equations whose principal part depends nonlinearly on the gradient of the state y

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

on quotients of hom functors and representations of finite general linear groups i abstract this is a second article on quotients of hom functors and their applications to the representation theory of finite general linear groups in a nondescribing characteristic after some general results on quotients of hom functors and their connection to the harish chandra theory these constructions are used to obtain a full classification of the l modular irreducible representations of gl n q for some prime power q which is not divisible by the prime l and to explain some facts on their harish chandra series and decomposition numbers

d optimal split plot designs with given numbers and sizes of whole plots the design of split plot experiments has received considerable attention during the last few years the goal of this article is to provide an efficient algorithm to compute d optimal split plot designs with given numbers of whole plots and given whole plot sizes the algorithm is evaluated and applied to a protein extraction experiment in addition it is shown that two level factorial and fractional factorial designs are d optimal for estimating first order response surface models for specific numbers and sizes of whole plots

state constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions we consider a control and state constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions these conditions occur during the modeling of diffuse gray conductive radiative heat transfer the nonlocal radiation interface condition and the pointwise state constraints represent the particular features of this problem to deal with the state constraints continuity of the state is shown which allows us to derive first order necessary conditions afterwards we establish second order sufficient conditions that account for strongly active sets and ensure local optimality in an l 2 neighborhood

post fractionated strip block designs novel arrangements for strip block designs that reduce the experimental effort are presented theoretical properties of strip block designs using post fractionation are provided and appropriate data analysis is explained an experiment on an industrial process is used as an illustration as a tool to aid the selection of appropriate plans catalogs of post fractionated strip block designs with 16 and 32 trials are provided

filtrations in rouquier blocks of symmetric groups and schur algebras we study rouquier blocks of symmetric groups and schur algebras in detail and obtain explicit descriptions for the radical layers of the principal indecomposable weyl young and specht modules of these blocks at the same time the jantzen filtrations of the weyl modules are shown to coincide with their radical filtrations we also address the conjectures of martin lascoux leclerc thibon rouquier and james for these blocks

second order elliptic equations with mixed boundary conditions we consider the mixed boundary value problem au f in b0u g0 in b1u g1in where is a bounded open subset of rn whose boundary is divided into disjoint open subsets and by an n 2 dimensional manifold in we assume a is a properly elliptic second order partial differential operator on and bj for j 0 1 is a normal jth order boundary operator satisfying the complementing condition with respect to a on the coefficients of the operators and and are all assumed arbitrarily smooth as announced in bull amer math soc 83 1977 391 393 we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in sobolev spaces in fact we construct an open subset t of the reals such that if ds u hs au 0 then for s 12 mod 1 b0 b1 ds hs 12 hs 32 is a fredholm operator if and only if s t moreover t xew tx where the sets tx are determined algebraically by the coefficients of the operators at x if n 2 tx is the set of all reals not congruent modulo 1 to some exceptional value if n 3 tx is either an open interval of length 1 or is empty and finally if n 4 tx is an open interval of length 1

the principal 3 blocks of four and five dimensional projective special linear groups in non defining characteristic abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he has conjectured that for any prime p if a finite group g has an abelian sylow p subgroup p then the principal p blocks of g and the normalizer ng p of p in g are derived equivalent let q be a power of a prime such that q 2 or 5 mod 9 in this paper we show that broue s conjecture is true for p 3 and for g psl4 q and g psl5 q in these cases g has elementary abelian sylow 3 subgroups of order 9 what we prove here is the following in the case g psl4 q all the principal 3 blocks of g are morita even puig equivalent independently of infinitely many q in the case g psl5 q all the principal 3 blocks of g are morita even puig equivalent to the principal 3 block of ng p independently of infinitely many q

rouquier blocks in chevalley groups of type e abstract in finite chevalley groups of type e we shall find a rouquier like block algebra in non defining characteristic we construct a morita equivalence between this block and a principal block of a local subgroup as an application of the equivalence we shall determine some decomposition numbers in type e

applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients the paper concerns dirichlet s problem for second order quasilinear non divergence form elliptic equations with discontinuous coefficients we start with suitable structure growth and regularity conditions ensuring solvability of the problem under consideration fixing then a solution u 0 such that the linearized at u 0 problem is non degenerate we apply the implicit function theorem as a result we get that for all small perturbations of the coefficients there exists exactly one solution u u 0 which depends smoothly in w 2 p with p larger than the space dimension on the data for that no structure and growth conditions are needed and the perturbations of the coefficients can be general l functions of the space variable x moreover we show that the newton iteration procedure can be applied in order to obtain a sequence of approximate in w 2 p solutions for u 0

quasi optimal convergence rate for an adaptive finite element method we analyze the simplest and most standard adaptive finite element method afem with any polynomial degree for general second order linear symmetric elliptic operators as is customary in practice the afem marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property we prove that the afem is a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops this geometric decay is instrumental to derive the optimal cardinality of the afem we show that the afem yields a decay rate of the energy error plus oscillation in terms of the number of degrees of freedom as dictated by the best approximation for this combined nonlinear quantity

convergence and quasi optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems recently an adaptive nonconforming finite element method anfem has been developed by carstensen and hoppe in numer math 103 251 266 2006 in this paper we extend the result to some nonsymmetric and indefinite problems the main tools in our analysis are a posteriori error estimators and a quasi orthogonality property in this case we need to overcome two main difficulties one stems from the nonconformity of the finite element space the other is how to handle the effect of a nonsymmetric and indefinite bilinear form an appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order crouzeix raviart element it is shown that the anfem is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops moreover quasi optimality in the sense of quasi optimal algorithmic complexity can be shown for the anfem the results of numerical experiments confirm the theoretical findings

new approach to the incompressible maxwell boussinesq approximation existence uniqueness and shape sensitivity abstract the boussinesq approximation to the fourier navier stokes f n s flows under the electromagnetic field is considered such a model is the so called maxwell boussinesq approximation we propose a new approach to the problem we prove the existence and uniqueness of weak solutions to the variational formulation of the model some further regularity in w 1 2 0 is obtained for the weak solutions the shape sensitivity analysis by the boundary variations technique is performed for the weak solutions as a result the existence of the strong material derivatives for the weak solutions of the problem is shown the result can be used to establish the shape differentiability for a broad class of shape functionals for the models of fourier navier stokes flows under the electromagnetic field

error estimates for optimal control problems of a class of quasilinear equations arising in variable viscosity fluid flow we consider optimal control problems of quasilinear elliptic equations with gradient coefficients arising in variable viscosity fluid flow the state equation is monotone and the controls are of distributed type we prove that the control to state operator is twice frechet differentiable for this class of equations a finite element approximation is studied and an estimate of optimal order h is obtained for the control the result makes use of the distributed structure of the controls together with a regularity estimate for elliptic equations with holder coefficients and a second order sufficient optimality condition the paper ends with a numerical experiment where the approximation order is computationally tested

splendid equivalences derived categories and permutation modules we introduce the notion of a splendid equivalence between blocks of finite groups which is a strengthening of the notion of an equivalence of derived categories such an equivalence is always induced by a two sided tilting complex whose terms are summands of permutation modules a feature that is compatible with the belief that these complexes should be related to the adic cohomology of deligne lusztig varities in the case of reductive groups over finite fields we show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence in particular it gives for principal blocks a structural explanation of brou s concept of an isotypy a compatible family of perfect isometries we give several examples including examples of morita equivalences that are splendid in an unexpectedly non trivial way

measure valued directional sparsity for parabolic optimal control problems a directional sparsity framework allowing for measure valued controls in the spatial direction is proposed for parabolic optimal control problems it allows for controls which are localized in space where the spatial support is independent of time well posedness of the optimal control problems is established and the optimality system is derived it is used to establish structural properties of the minimizer an a priori error analysis for finite element discretization is obtained and numerical results illustrate the effects of the proposed cost functional and the convergence results

equivalent blocks of finite general linear groups in non describing characteristic abstract j chuang r kessar and j rickard have proved broue s abelian defect group conjecture for many symmetric groups we adapt the ideas of kessar and chuang towards finite general linear groups represented over non describing characteristic we then describe morita equivalences between certain p blocks of gl n q with defect group c p c p as q varies see theorem 2 here p and q are coprime this generalizes work of s koshitani and m hyoue who proved the same result for principal blocks of gl n q when p 3 1 in a different way

aw1 p estimate for solutions to mixed boundary value problems for second order elliptic differential equations on demontre que sous des hypotheses plutot faibles une solution d un probleme aux valeurs limites mixte pour une equation elliptique d ordre 2 est dans l espace de sobolev w 1 p pour p 2

optimal control for the thermistor problem this paper is concerned with the state constrained optimal control of the two dimensional thermistor problem a quasi linear coupled system of a parabolic and elliptic pde with mixed boundary conditions this system models the heating of a conducting material by means of direct current existence uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity by similar arguments the linearized state system is discussed while the adjoint system involving measures is investigated using a duality argument these results allow us to derive first order necessary conditions for the optimal control problem

the decomposition numbers of the hecke algebra of type letw be the finite coxeter group of typef4 andhr q be the associated hecke algebra with parameter a prime powerq defined over a valuation ringr in a large enough extension field ofq with residue class field of characteristicr in this paper ther modular decomposition numbers ofhr q are determined for allq andr such thatr does not divideq the methods of the proofs involve the study of the generic hecke algebra of typef4 over the ringa u1 2 u 1 2 of laurent polynomials in an indeterminateu1 2 and its specializations onto the ring of integers in various cyclotomic number fields substancial use of computers and computer program systems gap maple meat axe has been made

integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions abstract equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered the bounded domain is assumed to have a lipschitz boundary and to satisfy additional regularity assumptions w 1 p regularity for the displacements and l p regularity for the stresses are proved for some p 2

the design and analysis of 2 k p s prototype experiments israel prototype testing and experimentation play a key role in the development of new products it is common practice to build a single prototype product and then test it at specified operating conditions it is often beneficial however to make several variants of a prototype according to a fractional factorial design the information obtained can be important in comparing design options and improving product performance and quality in such experiments the response of interest is often not a single number but a performance curve over the test conditions in this article we develop a general method for the design and analysis of prototype experiments that combines orthogonal polynomials with two level fractional factorials the proposed method is simple to use and has wide applicability we explain our ideas by reference to an experiment reported by taguchi on carbon monoxide exhaust of combustion engines we then apply them to an experiment on a prototype fluid flow controller

adaptive finite element methods for the stokes problem with discontinuous viscosity discontinuity in viscosities is of interest in many applications classical adaptive numerical methods perform under the restricting assumption that the discontinuities of the viscosity are captured by the initial partition this excludes applications where the jump of the viscosity takes place across curves manifolds or at a priori unknown positions we present a novel estimate measuring the distortion of the viscosity in lq for a q 2 we show that the latter holds on any bounded lipschitz domain provided the data belongs to a smaller class than those required to obtain well posedness based on this theory we introduce adaptive finite element methods which approximate the solution of stokes equations with possible discontinuous viscosities we prove that these algorithms are quasi optimal in terms of error compared to the number of cells finally the performance of the adaptive algorithm is numerically illustrated on insightful examples

the poisson problem with mixed boundary conditions in sobolev and besov spaces in non smooth domains we introduce certain sobolev besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in lipschitz domains in particular these are used to obtain sharp well posedness results for the poisson problem for the laplacian with mixed boundary conditions on bounded lipschitz domains which satisfy a suitable geometric condition introduced by r brown in 1994 in this context we obtain results which generalize those by d jerison and c kenig 1995 as well as e fabes o mendez and m mitrea 1998 applications to hodge theory and the regularity of green operators are also presented

optimal control of static elastoplasticity in primal formulation an optimal control problem of static plasticity with linear kinematic hardening and von mises yield condition is studied the problem is treated in its primal formulation where the state system is a variational inequality of the second kind first order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by huber type smoothing and a subsequent limit analysis the equivalence of the optimality conditions with the c stationarity system for the equivalent dual formulation of the problem is proved numerical experiments are presented which demonstrate the viability of the huber type smoothing approach

designing experiments for causal networks causal networks are directed graphs representing cause effect relationships and are multiple response generalizations of ishikawa s cause effect diagrams emphasizing tolerance design applications this article describes an algorithm for designing suitable experiments when the factors and responses are organized as a causal network the causal network is transformed into a so called causal map which represents all factors and responses as points in a common d dimensional metric space the design approach is algorithmic optimizing the entropy criterion due to wynn this criterion is applied to maximize dispersion among the multiple responses using a distance in space coefficients model a key constraint is for the blocks to be self contained this implies that each block can be analyzed without reference to other blocks this is to be complemented by a unified all block analysis the resulting designs are evaluated for efficiency response dispersion and resolution v column rank particular attention

smooth bifurcation branches of solutions for a signorini problem abstract we study a bifurcation problem for the equation u u g u u 0 on a rectangle with signorini boundary conditions on a part of one edge and mixed zero dirichlet and neumann boundary conditions on the rest of the boundary here r is the bifurcation parameter and g is a small perturbation we prove under certain assumptions concerning an eigenfunction u 0 corresponding to an eigenvalue 0 of the linearized equation with the same nonlinear boundary conditions the existence of a local smooth branch of nontrivial solutions bifurcating from the trivial solutions at 0 in the direction of u 0 the contact sets of these nontrivial solutions are intervals which change smoothly along the branch the main tool of the proof is a local equivalence of the unilateral bvp to a system consisting of a corresponding classical bvp and of two scalar equations to this system classical crandall rabinowitz type local bifurcation techniques scaling and implicit function theorem are applied

global existence uniqueness and stability for nonlinear dissipative bulk interface interaction systems abstract we show global well posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk interface systems they correspond to thermodynamically consistent gradient structure models of bulk interface interaction the setting includes nonlinear slow and fast diffusion in the bulk and nonlinear coupled diffusion on the interface additional driving mechanisms can be included and non smooth geometries and coefficients are admissible to some extent an important application are volume surface reaction diffusion systems with nonlinear coupled diffusion

classical solutions of drift diffusion equations for semiconductor devices the two dimensional case abstract we regard drift diffusion equations for semiconductor devices in lebesgue spaces to that end we reformulate the generalized van roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes this evolution equation falls into a class of quasi linear parabolic systems which allow unique local in time solution in certain lebesgue spaces in particular it turns out that the divergence of the electron and hole currents is an integrable function hence gauss theorem applies and gives the foundation for space discretization of the equations by means of finite volume schemes moreover the strong differentiability of the electron and hole density in time is constitutive for the implicit time discretization scheme finite volume discretization of space and implicit time discretization are accepted custom in engineering and scientific computing this investigation puts special emphasis on non smooth spatial domains mixed boundary conditions and heterogeneous material compositions as required in electronic device simulation