Global comparison principles for the $p$-Laplace operator on Riemannian manifolds

TL;DR

This paper establishes global comparison principles for the $p$-Laplacian on $p$-parabolic Riemannian manifolds, applicable to real-valued and vector-valued maps with finite $p$-energy, advancing understanding of nonlinear PDEs on manifolds.

Contribution

It introduces new global comparison results for the $p$-Laplacian on $p$-parabolic manifolds, extending previous local results to a broader geometric setting.

Findings

Proves comparison principles for the $p$-Laplacian on $p$-parabolic manifolds.

Applies to both real-valued and vector-valued maps with finite $p$-energy.

Enhances the theoretical framework for nonlinear PDEs on Riemannian manifolds.

Abstract

We prove global comparison results for the $p$-Laplacian on a $p$-parabolic manifold. These involve both real-valued and vector-valued maps with finite $p$-energy.