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

• Author(s): Manfredi, Juan J. ; Rossi, Julio D. ; Urbano, José Miguel
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11175
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): p(x)-Laplacian; Infinity-Laplacian; Variable exponents; Viscosity solutions
• Document Type: Preprint
• Language: English

Description

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.