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Artículo
Numerical approximation of a one-dimensional elliptic optimal design problem
(Society for Industrial and Applied Mathematics, 2011)
We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, ...
Artículo
A density result for the variation of a material with respect to small inclusions
(Elsevier, 2006-03-01)
We consider the family of materials obtained, via homogenization, by replacing a small portion, of size ɛ, of a fixed material by other materials. In a previous paper we have obtained a subset of the set of ‘derivatives’ ...
Artículo
Uniqueness results for pseudomonotone problems with p>2
(French Academy of Sciences, 2007-01-30)
We consider a pseudomonotone operator, the model of which is −div(b(x, u)|∇ u| p−2∇ u) with 1 <p< +∞ and b(x, s) a Lipschitz continuous function in s which hold satisfies 0 < α b(x, s) β < +∞. We show that the comparison ...
Artículo
The div-curl lemma “trente ans après”: an extension and an application to the G-convergence of unbounded monotone operators
(Elsevier, 2009-05)
In this paper new div-curl results are derived. For any open set Ω of RN, N⩾2, we study the limit of the product vn⋅wn where the sequences vn and wn are respectively bounded in Lp(Ω)N and Lq(Ω)N, while divvn and curlwn are ...
Artículo
Algunos trabajos relacionados con la teoría de E.D.P. y su homogeneización
(Sociedad Española de Matemática Aplicada, 2000-12)
Artículo
Homogenization of a quasi-linear problem with quadratic growth in perforated domains: An example
(Elsevier, 1997-01-01)
We study the homogenization of Dirichlet problems for a fixed quasi-linear operator which is the perturbation of the Laplace operator by the square of the gradient, when the domain varies arbitrarily. With respect to the ...
Artículo
Asymptotic behaviour of equicoercive diffusion energies in dimension two
(Springer, 2007-08)
In this paper, we study the asymptotic behaviour of a given equicoercive sequence of diffusion energies Fn, n ∈ N, defined in L2(Ω), for a bounded open subset Ω of R2. We prove that, contrary to the three dimension (or ...
Artículo
Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material
(SIAM, 2021-01-01)
For a diffusion problem modeled by thep-Laplacian operator, we are interested inobtaining numerically the two-phase material which maximizes the internal energy. We assume thatthe amount of the best material is limited. ...
Artículo
Homogenization of systems with equi-integrable coefficients
(EDP Sciences, 2014)
In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability ...
Artículo
Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
(Society for Industrial and Applied Mathematics, 2013)
We study the asymptotic behavior of the solutions of the Navier–Stokes system in a thin domain Ωε of thickness ε satisfying the Navier boundary condition on a periodic rough set Γε ⊂ ∂Ωε of period rε and amplitude δε, with ...