ESTIMATIVAS LOCAIS PARA SOLUÇÕES POSITIVAS DO P-LAPLACIANO

Abstract

RESUMO Neste trabalho consideramos o problema de Dirichlet para soluções positivas da equação p-Laplaciano em um domínio, limitado e suave no espaço euclidiano. Estudamos a técnica iterativa de Moser (Comm. Pure Appl. Math., vol.14 (1961), 577-591 ) melhorada por Trudinger em (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), vol.27 (1973), 265-308), a partir da qual fazemos estimativas locais para solu¸c˜oes do operador linearizado associado,e para solu¸c˜oes do problema. Este trabalho ´e baseado nos seguintes artigos: “Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of p laplace equations” de Lucio Damascelli e Berardino Sciunzi (Calc. Var. Partial Differential Equations, vol.25 (2005), 139-159); “A Strong Comparison Principle for the p–Laplacian” of Paolo Roselli and Berardino Sciunzi (Proc. Amer. Math. Soc. vol.135 (2007), 3217-3224). Abstract In this work we consider the Dirichlet problem for positive solutions of p-Laplacian equa tion on a smooth bounded domain in the euclidean space. We studied the Moser’s itera tive technique (Comm. Pure Appl. Math., vol.14 (1961), 577-591) improved by Trudinger (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), vol.27 (1973), 265-308) from which we make local estimates for the solutions of the associated linearized operator, and for solutions of the problem. This work is based on the following articles: “Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of p-laplace equations” of Lucio Damascelli and Berardino Sciunzi (Calc. Var. Partial Differential Equations, vol.25 (2005), 139-159); “A Strong Comparison Principle for the p–Laplacian” of Paolo Roselli and Berardino Sciunzi (Proc. Amer. Math. Soc. vol.135 (2007), 3217-3224).