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.
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Harjulehto et al. (2019) studied this question.
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