A new approach to Liouville theorems for elliptic inequalities

TL;DR

This paper reviews a novel method for establishing Liouville theorems, demonstrating the nonexistence of positive solutions to elliptic inequalities involving p-Laplacian or Pucci operators in unbounded domains.

Contribution

The authors introduce a new approach for proving Liouville theorems, applicable to elliptic inequalities with p-Laplacian and Pucci operators, expanding existing theoretical tools.

Findings

Established nonexistence results for p-Laplacian inequalities

Extended Liouville theorems to Pucci extremal operators

Provided a unified framework for elliptic inequalities in unbounded domains

Abstract

In this article we review a new method for proving the nonexistence of positive solutions of elliptic inequalities in unbounded domains in $\rn$, which was recently introduced by the authors. We expose our method and new results on the two most frequently encountered cases: inequalities involving the p-Laplacian or the Pucci extremal operator.