Boundary limits of monotone Sobolev functions for double phase functionals

Abstract

Our aim in this paper is to deal with boundary limits of monotone Sobolev functions for the double phase functional $\Phi_{p,q}(x,t) = t^{p} + (b(x) t)^{q}$ in the unit ball ${\bf B}$ of ${\mathbb R}^n$, where 1 < $p$ < $q$ < $\infty$ and $b(\cdot)$ is a non-negative bounded function on ${\bf B}$ which is Hölder continuous of order $\theta \in (0,1]$.