Strong maximum principles for fractional Laplacians

TL;DR

This paper develops a unified framework for strong maximum principles applicable to various nonlocal operators of order s in (0,1), including different types of fractional Laplacians.

Contribution

It introduces a comprehensive approach that covers multiple nonlocal Laplacian operators, extending maximum principles to a broader class of fractional operators.

Findings

Established strong maximum principles for Dirichlet fractional Laplacians.

Extended maximum principles to Neumann Restricted and Semirestricted Laplacians.

Unified approach simplifies analysis of nonlocal operators.

Abstract

We give a unified approach to strong maximum principles for a large class of nonlocal operators of the order $s\in(0,1)$, that includes the Dirichlet, the Neumann Restricted (or Regional) and the Neumann Semirestricted Laplacians.