Regularity to Thin Obstacle Problem in Orlicz spaces

TL;DR

This paper proves regularity properties, including Lipschitz and Hölder continuity of gradients, for solutions to the thin obstacle problem in Orlicz spaces, using De Giorgi's techniques.

Contribution

It introduces regularity results for the thin obstacle problem in Orlicz spaces, extending classical theories to more general functional settings.

Findings

Minimizers are Lipschitz continuous.

Gradients of minimizers are Hölder continuous.

Characterization of nodal set structures.

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.