Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials

TL;DR

This paper establishes precise nonexistence results for nonnegative distributional supersolutions of linear elliptic equations with Hardy and Leray potentials, highlighting the critical thresholds where solutions cannot exist.

Contribution

It provides sharp nonexistence criteria for elliptic equations involving inverse-square potentials and logarithmic weights, advancing understanding of such singular problems.

Findings

Sharp nonexistence results for supersolutions.

Identification of critical thresholds for solution existence.

Enhanced understanding of elliptic equations with singular potentials.

Abstract

In this paper we deal with nonnegative distributional supersolutions for a class of linear elliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.