A comparison principle for nonlinear heat Rockland operators on graded groups

Abstract

In this note we show a comparison principle for nonlinear heat Rockland operators on graded groups. We give a simple proof for it using purely algebraic relations. As an application of the established comparison principle we prove the global in $t$-boundedness of solutions for a class of nonlinear equations for the heat $p$-sub-Laplacian on stratified groups.

arXiv commentto appear in Bulletin of London Mathematical Society

References in corpus (2)

• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups
• The existence of a global fundamental solution for homogeneous Hörmander operators via a global lifting method

Cited by in corpus (3)

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• Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups
• Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group