Optimal design problems for a degenerate operator in Orlicz-Sobolev spaces

Autor(es)

Santos, Jefferson Abrantes ; Soares, Sergio H. Monari

• Tipo de documento: Artigo Científico
• Fonte: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 59, n. 6, p. 23-pg., 2020-10-08.

Resumo

An optimization problem with volume constraint involving the Phi-Laplacian in Orlicz-Sobolev spaces is considered for the case where Phi does not satisfy the natural condition introduced by Lieberman. A minimizer u(Phi) having non-degeneracy at the free boundary is proved to exist and some important consequences are established like the Lipschitz regularity of uF along the free boundary, that the set {u(Phi) > 0} has uniform positive density, that the free boundary is porous with porosity delta > 0 and has finite (N - delta)-Hausdorff measure. Under a geometric compatibility condition set up by Rossi and Teixeira, it is established the behavior of a l-quasilinear optimal design problem with volume constraint for l small. As l -> 0(+), we obtain a limiting free boundary problem driven by the infinity-Laplacian operator and find the optimal shape for the limiting problem. The proof is based on a penalization technique and a truncated minimization problem in terms of the Taylor polynomial of Phi. (AU)

• Processo FAPESP: 18/11664-0 - Problemas quasilineares em espaços de Orlicz-Sobolev
• Beneficiário: Sergio Henrique Monari Soares
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil
• Processo FAPESP: 16/16745-3 - Problema limite de fronteira livre em espaços de Orlicz-Sobolev
• Beneficiário: Sergio Henrique Monari Soares
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil