Regularity of the solutions to a nonlinear boundary problem with indefinite weight
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 ∈]0, 1[, and V is a weight in...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2011-01-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11402/6172 |
| Summary: | 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 ∈]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 regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega}) for some alpha ∈ ]0, 1[. |
|---|---|
| ISSN: | 0037-8712 2175-1188 |