Analysis reveals boundary regularity for fractional p-Laplace equations in nonsmooth domains, suggesting novel findings in analysis.
We consider nonhomogeneous fractional p-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish several fine boundary regularity results for solutions, and their gradient, near the boundary. To the best of our knowledge, each of our results is new even in the linear case.
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Byun et al. (2025) studied this question.
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