Limits as p(x) of p(x)-harmonic functions

• Autor(es): Manfredi, Juan J. ; Rossi, Julio D. ; Urbano, José Miguel
• Data: 2009
• Identificador Persistente: http://hdl.handle.net/10316/11175
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): p(x)-Laplacian; Infinity-Laplacian; Variable exponents; Viscosity solutions
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

In this note we study the limit as p(x) ! 1of solutions to − p(x)u = 0 in a domain , with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +1 and analyzing how the corresponding solutions of the problem converge and what equation is satisfied by the limit.