Boundary regularity under generalized growth conditions

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>We study the Dirichlet ϕ-energy integral with Sobolev boundary values. The function ϕ has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfied for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.</p></div>