On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results

TL;DR

This paper investigates fractional elliptic equations in unbounded Lipschitz domains with epigraph properties, establishing symmetry, monotonicity, and rigidity results, including for halfspaces and flat at infinity epigraphs.

Contribution

It provides new regularity, monotonicity, and symmetry results for nonlocal fractional elliptic equations in unbounded Lipschitz domains with epigraph structures.

Findings

Proves symmetry and monotonicity in specific unbounded domains.

Establishes rigidity results for fractional elliptic equations.

Analyzes equations in halfspaces and flat at infinity epigraphs.

Abstract

We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity.