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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Bibliographic Details
Author: Clemente, Rodrigo Genuino
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
Description
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.