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

Abstract

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.