Bounded weak solutions to nonlinear elliptic equations.
Boundedness and continuity of solutions to linearelliptic boundary value problems in two dimensions.
Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions.
Boundedness of the solution of the third problem for the Laplace equation
A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.
Bounds for elliptic operators in weighted spaces.
Bounds of Riesz Transforms on Spaces for Second Order Elliptic Operators
Let -div be a second order elliptic operator with real, symmetric, bounded measurable coefficients on or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform on the space. As an application, for , we establish the boundedness of Riesz transforms on Lipschitz domains for operators with coefficients. The range of is sharp. The closely related boundedness of ...
Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations
regularity for elliptic equations with the general nonstandard growth conditions
We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on . We prove the global regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.
Calcul des singularités par la méthode des éléments finis
Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux)
Dans cet article, on considère les opérateurs différentiels , où et sont deux fonctions mesurables, bornées et accrétives, et . Les résultats principaux portent sur les propriétés fonctionnelles de , de sa racine carrée, avec applications à l’équation elliptique sur . On démontre que est un opérateur de Calderón-Zygmund qui dépend analytiquement du couple . Les estimations ponctuelles optimales sur le noyau du semi-groupe et le calcul fonctionnel permettent de développer une théorie...
Caractérisation de classes de fonctions par des itères d’opérateurs elliptiques dégénérés sur des ouverts irréguliers
Cell centered Galerkin methods for diffusive problems
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces in discrete...
Cell centered Galerkin methods for diffusive problems
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces...
Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...
Coerciveness inequality for nonlocal boundary value problems for second order abstract elliptic differential equations.
Compactness results for Ginzburg-Landau type functionals with general potentials.
Comparing multilevel coarsening strategies.
Comparison of a genetic algorithm and a gradient based optimisation technique for the detection of subsurface inclusions.
Comparison of Linear System Solvers Applied to Diffusion-Type Finite Element Equations.
Comparison results for elliptic and parabolic equations via Schwarz symmetrization