Indefinite fractional elliptic problem and Liouville theorems

TL;DR

This paper studies indefinite fractional elliptic equations, establishing Liouville-type theorems, deriving a priori bounds for solutions, and classifying solutions of related degenerate elliptic equations derived from the fractional Laplacian.

Contribution

It introduces new Liouville-type theorems for indefinite fractional elliptic problems and classifies solutions of related degenerate elliptic equations.

Findings

Liouville-type theorems for indefinite fractional elliptic equations

A priori bounds for solutions in bounded domains

Classification of solutions for degenerate elliptic equations

Abstract

In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded domain by blowing-up and re-scaling. We also classify the solutions of some degenerate elliptic equation originated from fractional Laplacian.