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Artículo
A characterization result for the existence of a two-phase material minimizing the first eigenvalue
(Elsevier, 2016-09-19)
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 ...
Artículo
Semilinear problems with right-hand sides singular at u = 0 which change sign
(Elsevier, 2021-06-01)
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. ...
Artículo
Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains
(Elsevier, 1997-05)
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. ...
Artículo
Asymptotic behavior of nonlinear elliptic systems on varying domains
(Society for Industrial and Applied Mathematics, 2000)
We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, ...
Artículo
Homogenization of convex functionals which are weakly coercive and not equi-bounded from above
(Elsevier, 2013-08-01)
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, ...
Artículo
Homogenization of non-uniformly bounded periodic diffusion energies in dimension two
(IOP Publishing, 2009)
This paper deals with the homogenization of two-dimensional oscillating convex functionals, the densities of which are equicoercive but not uniformly bounded from above. Using a uniform-convergence result for the minimizers, ...
Artículo
Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design
(Elsevier, 2006-07-15)
In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients and the domains vary arbitrarily. Here, we improve the convergence result given in this paper ...
Artículo
On existence of optimal potentials on unbounded domains
(Cornell University, 2019-09-13)
We consider elliptic equations of Schrödinger type with a right-hand side fixed and with the linear part of order zero given by a potential V . The main goal is to study the optimization problem for an integral cost depending ...
Artículo
On the Navier boundary condition for viscous fluids in rough domains
(Sociedad Española de Matemática Aplicada, 2012-04)
In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough domains assuming Navier boundary conditions on the rough boundary. Our main interest is to study the ...
Artículo
The maximization of the p-Laplacian energy for a two-phase material
(SIAM Publications Library, 2021)
We consider the optimal arrangement of two diffusion materials in a bounded openset \Omega \subset \BbbR Nin order to maximize the energy. The diffusion problem is modeled by thep-Laplacianoperator. It is well known that ...