On nonnegative solutions of the parabolic differential inequality with $(p,q)$-Laplace on Riemannian manifolds

TL;DR

This paper proves nonexistence of solutions for certain parabolic inequalities involving the $(p,q)$-Laplacian on Riemannian manifolds, using test functions and volume growth conditions.

Contribution

It extends Liouville-type theorems to a broader class of parabolic inequalities with $(p,q)$-Laplacian on Riemannian manifolds.

Findings

Nonexistence results under weighted volume growth assumptions

Broader class of parabolic inequalities analyzed

Method based on test function argument

Abstract

In this paper, we establish Liouville-type theorems for parabolic differential inequalities with $(p,q)-$Laplacian operator on Riemannian manifolds. By a test function argument, we establish nonexistence results under suitable weighted volume growth assumptions involving potential. In particular, we can obtain nonexistence results for a wider class of parabolic inequalities.