Boundary pointwise regularity and applications to the regularity of free boundaries

TL;DR

This paper develops boundary pointwise regularity results for Dirichlet and oblique derivative problems, providing simpler proofs for the higher regularity of free boundaries in obstacle and one-phase problems.

Contribution

It introduces new boundary regularity results and applies them to establish higher regularity of free boundaries with simpler proofs.

Findings

Boundary pointwise regularity for Dirichlet problems

Boundary pointwise regularity for oblique derivative problems

Simplified proofs of free boundary regularity

Abstract

In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the higher regularity of the free boundaries in obstacle-type problems and one phase problems.