In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domain Omega ⊂ 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 ∈]0, 1[, and V is a weight in L^s(partial Omega) and h ∈ L^s(partial Omega ) for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega) cap L^{infty}(Omega), and using the D.Debenedetto’s theorem of regularityin [1] we conclude that those solutions are in C^{1,alpha} overline{Omega}) for some alpha ∈ ]0, 1[.
@article{11402,
title = {Regularity of the solutions to a nonlinear boundary problem with indefinite weight - doi: 10.5269/bspm.v29i1.11402},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {28},
year = {2010},
doi = {10.5269/bspm.v29i1.11402},
language = {EN},
url = {http://dml.mathdoc.fr/item/11402}
}
Anane, Aomar; Chakrone, Omar; Moradi, Najat. Regularity of the solutions to a nonlinear boundary problem with indefinite weight - doi: 10.5269/bspm.v29i1.11402. Boletim da Sociedade Paranaense de Matemática, Tome 28 (2010) . doi : 10.5269/bspm.v29i1.11402. http://gdmltest.u-ga.fr/item/11402/