Regularidade de Soluções de Uma Classe de Problemas Elípticos Semi-lineares
We start studing semi-stable solutions for the equation u = f(u) in a smooth and bounded domain of Rn, 2 n 4. The presented result is a L1 boundedness, which holds for all semi-stable positive solution and all non-linearity f. We also show a approach about the case u = f(u) in the unitary ball of Rn...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | Brasil |
| Institution: | Universidade Federal da Paraíba (UFPB) |
| Repository: | Biblioteca Digital de Teses e Dissertações da UFPB |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufpb.br:tede/7396 |
| Online Access: | https://repositorio.ufpb.br/jspui/handle/tede/7396 |
| Access Level: | Open access |
| Keyword: | Problemas elípticos semi lineares Soluções semi-estáveis Domínio suave limitado Semilinear elliptic problems Semi-stable solutions Limited soft domain CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Summary: | We start studing semi-stable solutions for the equation u = f(u) in a smooth and bounded domain of Rn, 2 n 4. The presented result is a L1 boundedness, which holds for all semi-stable positive solution and all non-linearity f. We also show a approach about the case u = f(u) in the unitary ball of Rn. The results obtained are Lq and Wk;q estimates for semi-stable radial solutions u 2 H1 0 , the proof of a boundedness if n 9 and, in case that g is increasing and convex, u 2 W3;2 in all dimension n. |
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