Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2019-01-07
Boundary Regularity under Generalized Growth ConditionsPetteri Harjulehto and Peter Hästö (1) University of Turku, Finland
(2) University of Turku and University of Oulu, Finland
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.
Keywords: Dirichlet energy integral, regular boundary point, minimizer, superminimizer, generalized Orlicz space, Musielak–Orlicz spaces, the weak Harnack inequality, nonstandard growth, variable exponent, double phase
Harjulehto Petteri, Hästö Peter: Boundary Regularity under Generalized Growth Conditions. Z. Anal. Anwend. 38 (2019), 73-96. doi: 10.4171/ZAA/1628