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.