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|Type:||Artigo de periódico|
|Title:||Existence and regularity properties of non-isotropic singular elliptic equations|
de Queiroz, OS
|Abstract:||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.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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