Higher Regularity of the Free Boundary in the Obstacle Problem for the Fractional Laplacian

TL;DR

This paper establishes higher regularity of the free boundary in the obstacle problem involving the fractional Laplacian by employing advanced boundary Harnack inequalities.

Contribution

It introduces a higher order boundary Harnack inequality to prove improved regularity results for the free boundary in the fractional Laplacian obstacle problem.

Findings

Higher regularity of the free boundary achieved

Development of a higher order boundary Harnack inequality

Enhanced understanding of free boundary behavior in fractional Laplacian problems

Abstract

We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.