Boundary Regularity under Generalized Growth Conditions



: Harjulehto P, Hästö P

Publisher: EUROPEAN MATHEMATICAL SOC

: 2019

: Zeitschrift für Analysis und ihre Anwendungen

: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN

: Z ANAL ANWEND

: 38

: 1

: 73

: 96

: 24

: 0232-2064

: 1661-4534

DOI: https://doi.org/10.4171/ZAA/1628


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 satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.



Last updated on 2024-26-11 at 13:50