Boundary regularity and non-transversal intersection for the fully nonlinear obstacle problem

TL;DR

This paper proves non-transversal intersection of free and fixed boundaries in fully nonlinear obstacle problems across all dimensions, establishes $C^1$ regularity of the free boundary, and classifies blow-up solutions.

Contribution

It extends boundary regularity and intersection results to fully nonlinear obstacle problems, providing new regularity and classification theorems.

Findings

Non-transversal intersection holds in any dimension.

$C^1$ regularity of the free boundary is established.

A classification of blow-up solutions is provided.

Abstract

In this paper non-transversal intersection of the free and fixed boundary is shown to hold in any dimension for obstacle problems generated by fully nonlinear uniformly elliptic operators. Moreover, $C^1$ regularity results of the free boundary are obtained and a classification of blow-up solutions is given.