Abstract:We establish boundary Hölder 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 \(\alpha\)-Hölder 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.
From: Alan Pio [view email]
[v1]
Fri, 12 Jun 2026 14:37:44 UTC (12 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。