%0 Journal Article
%T Regularity of the solutions to a nonlinear boundary problem with indefinite weight
%A Aomar Anane
%A Omar Chakrone
%A Najat Moradi
%J Boletim da Sociedade Paranaense de Matem¨¢tica
%D 2011
%I Sociedade Brasileira de Matem¨¢tica
%X In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p 2}u in the bounded smooth domainOmega   R^N,with| u|^{p 2} partial_{nu} u = lambda V (x)|u|^{p 2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ¡Ê]0, 1[, and V is a weight in L^s(partial Omega) and h ¡Ê L^s(partial Omega ) for some s ¡Ý 1. We prove that all solutions are in L^{infty}(Omega) cap L^{infty}(Omega), and using the D.Debenedetto¡¯s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega}) for some alpha ¡Ê ]0, 1[.
%K nonlinear boundary conditions
%K regularity of the solutions
%K indefinite weight.
%U http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11402/6172