Free boundary regularity near the fixed boundary for the fully nonlinear obstacle problem

TL;DR

This paper explores the regularity of free boundaries near fixed boundaries for fully nonlinear obstacle problems, extending interior theories to boundary contexts using novel approaches.

Contribution

It introduces a new method for analyzing free boundary regularity near fixed boundaries in fully nonlinear elliptic obstacle problems.

Findings

Established boundary regularity results for fully nonlinear obstacle problems.

Extended interior free boundary theory to boundary cases.

Provided new techniques for boundary regularity analysis.

Abstract

The interior free boundary theory for linear elliptic operators in higher dimensions was developed by Caffarelli in the low regularity context. In these notes, the up-to-the boundary free boundary regularity is discussed for nonlinear elliptic operators based on a different approach.