CASADO DÍAZ , Juan

In this paper, we study the homogenization of a Dirichlet problem in perforated domains for an operator which is the perturbation of the Laplace operator by a general nonlinear term with quadratic growth in the gradient. We show that a new term, which does not depend on the gradient, but which is nonlinear, appears in the limit problem. We also...

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En esta memoria se estudian dos problemas. El primero hace referencia a la relajación de un funcional energía sobre el cual no se imponen las hipótesis de coercividad y de acotación habituales. Esto lleva a efectuar el estudio para una topología de tipo Lebesgue y no de tipo Sobolev. Se obtiene un resultado parcial en el caso d-dimensional y un...

The present paper is devoted to obtaining some smoothness results for the solution of two classical control problems relative to the optimal mixture of two isotropic materials. In the first one, the goal is to maximize the energy. In the second one, we want to minimize the first eigenvalue of the corresponding elliptic operator. At least for...

We study the asymptotic behavior at infinity of the solutions of a nonlinear elliptic system posed in a cylinder of infinite length. The problem is written in a variational formulation, where we ask the derivative of the solutions to be in Lp. We show that an exponential decay at infinity for the second member implies exponential decay for the...

On étudie l'homogénéisation de problèmes de Dirichlet pour un opérateur quasi-linéaire fixe qui est la perturbation de l'opérateur de Laplace par le carré du gradient, pour une suite de domaines qui varient arbitrairement. Par rapport au problème de Laplace avec des conditions de Dirichlet posé sur les mêmes domaines, il apparaît un nouveau...

In un lavoro del 1982, D. Cioranescu e F. Murat hanno considerato il problema soddisfatto dal limite u di una successione un di soluzioni di 0 −∆un = f in Ωn, un = 0 su ∂Ωn, dove Ωn è una successione di insiemi aperti che sono contenuti in un fissato insieme aperto limitato Ω. Tale studio richiede di imporre numerose ipotesi sulla successione...

Given two isotropic homogeneous materials represented by two constants 0 <α< | |, we consider here the problem consisting in finding a mixture of these materials αχω + β(1 − χω), ω ⊂ RN measurable, with |ω| ≤ κ, such that the first eigenvalue of the operator u ∈ H1 0 ( ) → −divαχω + β(1 − χω) ∇u reaches the minimum value. In a recent paper,...

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This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using a pointwise estimate of the solutions combined with a two-dimensional capacitary estimate. We give two applications of...

This paper deals with the homogenization of nonlinear convex energies defined in W_{0}^{1,1}(\Omega )W01,1(Ω), for a regular bounded open set Ω of \mathbb{R}^{N}RN, the densities of which are not equi-bounded from above, and which satisfy the following weak coercivity condition: There exists q > N−1q>N−1 if N > 2N>2, and q⩾1q⩾1 if N = 2N=2,...

The paper deals with the homogenization of a magneto-elastodynamics equation satisfied by the displacement uεuε of an elastic body which is subjected to an oscillating magnetic field BεBε generating the Lorentz force ∂tuε×Bε∂tuε×Bε. When the magnetic field BεBε only depends on time or on space, the oscillations of BεBε induce an increase of...

The present paper is devoted to the study of the existence of a solution u for a quasilinear second order differential equation with homogeneous Dirichlet conditions, where the right-hand side tends to infinity at u = 0u=0. The problem has been considered by several authors since the 70's. Mainly, nonnegative right-hand sides were considered...