Existence and regularity properties of non-isotropic singular elliptic equations

Autor(es)

Montenegro, Marcelo ^[1] ; de Queiroz, Olivaine S. ^[1] ; Teixeira, Eduardo V. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ANNALEN; v. 351, n. 1, p. 215-250, SEP 2011.
• Citações Web of Science: 1

Resumo

We establish existence and sharp regularity results for solutions to singular elliptic equations of the order u(-beta), 0 < beta < 1, with gradient dependence and involving a forcing term lambda f (x, u). Our approach is based on a singularly perturbed technique. We show that if the forcing parameter lambda > 0 is large enough, our solution is positive. For lambda small solutions vanish on a nontrivial set and therefore they exhibit free boundaries. We also establish regularity results for the free boundary and study the asymptotic behavior of the problem as beta SE arrow 0 and beta NE arrow 1. In the former, we show that our solutions u(beta) converge to a C(1,1) function which is a solution to an obstacle type problem. When beta NE arrow 1 we recover the Alt-Caffarelli theory. (AU)

• Processo FAPESP: 08/01458-2 - Equações diferenciais parciais e fluxos de curvatura
• Beneficiário: Olivâine Santana de Queiroz
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado