arXiv subjects

Alan Pio Sousa

Publications and source records attributed to Alan Pio Sousa.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

Regularity to Thin Obstacle Problem in Orlicz spaces

In this work, we establish regularity results for minimizers of the energy functional associated with the thin obstacle problem in Orlicz spaces. More precisely, we prove the Lipschitz continuity and the Hölder continuity of the gradient of minimizers. The analysis is based on techniques from De Giorgi's classical regularity theory. As a byproduct of our results, we also provide a characterization of the structure of the nodal sets of the minimizers.

math.AP↗