Regularity of the solutions to a nonlinear boundary problem with indefinite weight

被引：6

作者：

Anane, Aomar ^{[1
]}

Chakrone, Omar ^{[1
]}

Moradi, Najat ^{[1
]}

机构：

[1] Univ Mohammed 1, Fac Sci, Dept Math & Informat, Oujda, Morocco

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2011年 / 29卷 / 01期

关键词：

Regularity; p-Laplacian; nonlinear boundary conditions; weight;

D O I：

10.5269/bspm.v29i1.11402

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the regularity of the solutions to the problem Delta(p)u = vertical bar u vertical bar(p-2)u in the bounded smooth domain Omega subset of R-N, with vertical bar del u vertical bar(p-2) partial derivative u/partial derivative v = lambda V(x)vertical bar u vertical bar(p-2)u+h as a nonlinear boundary condition where partial derivative Omega is C-2,C-beta with beta is an element of]0, 1[, and V is a weight in L-s(partial derivative Omega) and h is an element of L-s(partial derivative Omega) for some s >= 1. We prove that all solutions are in L-infinity(partial derivative Omega) boolean AND L-infinity(Omega), and using the D.Debenedetto's theorem of regularity in [1] we conclude that those solutions are C-1,C-alpha ((Omega) over bar) in for some alpha is an element of]0, 1[.

引用

页码：17 / 23

页数：7