H\"older regularity up to the boundary for the g-Laplacian on Reifenberg flat domains

Alan Pio Sousa

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arXiv · 2606.14505

H\"older regularity up to the boundary for the g-Laplacian on Reifenberg flat domains

Alan Pio Sousa

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Abstract

We establish boundary H\"older regularity for weak solutions to a class of nonlinear elliptic Dirichlet problems with nonstandard growth posed on Reifenberg flat domains. More precisely, for any prescribed exponent $\alpha\in(0,1)$, we show that weak solutions are $\alpha$-H\"older continuous up to the boundary provided that the Reifenberg flatness parameter is sufficiently small. The proof combines an iterative boundary decay argument with an ABP-type maximum principle in the Orlicz--Sobolev setting.

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Alan Pio Sousa. 2026-06-12. H\"older regularity up to the boundary for the g-Laplacian on Reifenberg flat domains. https://arxiv.org/abs/2606.14505

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