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

In this note we study the limit as p(x) → ∞ of solutions to −∆p(x)u = 0 in a domain Ω, with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +∞ and analyzing how the corresponding solutions of the problem converge and what equation is satisfied by the limit.Fil: Manfredi, Juan J.. University Of Pittsburgh; Estados UnidosFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Urbano, Jose Miguel. Universidad de Coimbra; Portuga