Hölder regularity up to the boundary for the g-Laplacian on Reifenberg flat domains

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 \(α\in(0,1)\), we show that weak solutions are \(α\)-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.