Nonexistence of distributional supersolutions of a semilinear elliptic equation with Hardy potential

TL;DR

This paper investigates the conditions under which non-negative distributional supersolutions do not exist for certain semilinear elliptic equations with Hardy potentials, highlighting the mathematical limitations of solutions in this context.

Contribution

It establishes nonexistence results for distributional supersolutions in semilinear elliptic equations with inverse-square potentials, extending previous theoretical understanding.

Findings

Nonexistence of supersolutions under specific conditions

Extension of Hardy potential theory in elliptic equations

Mathematical limitations identified for solution existence

Abstract

In this paper we study nonexistence of non-negative distributional supersolutions for a class of semilinear elliptic equations involving inverse-square potentials.