Regularity to Thin Obstacle Problem in Orlicz spaces
Analysis of PDEs
2026-02-05 v2
Abstract
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 H\"older 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.
Keywords
Cite
@article{arxiv.2602.01255,
title = {Regularity to Thin Obstacle Problem in Orlicz spaces},
author = {Junior da Silva Bessa and Paulo Henryque da Costa Silva and Alan Pio Sousa},
journal= {arXiv preprint arXiv:2602.01255},
year = {2026}
}
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