Artículos de revistas
A singular perturbation problem for the p(x)-Laplacian
Fecha
2013-06Registro en:
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A singular perturbation problem for the p(x)-Laplacian; Asociación Argentina de Matemática Aplicada, Computacional e Industrial; Matemática Aplicada Computacional e Industrial; 4; 6-2013; 485-488
2314-3282
Autor
Lederman, Claudia Beatriz
Wolanski, Noemi Irene
Resumen
We present results for the following singular perturbation problem:
∆p(x)uε := div(|∇uε(x)| p(x)−2∇uε) = βε(uε) + f ε, uε ≥ 0 (Pε(f ε))
in Ω ⊂ RN , where ε > 0, βε(s) = 1 εβ( s ε ), with β a Lipschitz function satisfying β > 0 in (0, 1), β ≡ 0 outside (0, 1) and β(s) ds = M. The functions uε and f ε are uniformly bounded. We prove uniform Lipschitz regularity, we pass to the limit (ε → 0) and we show that limit functions are weak solutions to a free boundary problem.