Limit as $p(x)\to \infty$ of $p(x)$-Harmonic functions for unbounded $p(x)$

Behzad Djafari Rouhani, Jan Lang, Osvaldo Méndez

It is shown that if $p_n$ is a sequence of continuous, unbounded exponents on a bounded, smooth domain $\Omega \subset {\mathbb{R}}^n$ with $1<\underset{x\in \Omega }{\inf }{p}_n(x)$ and $p_n\rightar…