We study the Dirichlet -energy integral with Sobolev boundary values. The function 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.
Cite this article
Petteri Harjulehto, Peter Hästö, Boundary Regularity under Generalized Growth Conditions. Z. Anal. Anwend. 38 (2019), no. 1, pp. 73–96DOI 10.4171/ZAA/1628