Boundary Regularity under Generalized Growth Conditions
Petteri Harjulehto, Peter Hästö · Zeitschrift für Analysis und ihre Anwendungen · 2019
We study the Dirichlet \phi -energy integral with Sobolev boundary values. The function \phi 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.