Another way to say harmonic

Abstract

This paper offers characterizations of subsolutions of the heat equation ut - Δu = 0 (the subcaloric functions) and the infinity heat equation ut - Δ∞u = 0 (the infinity-subcaloric functions) by means of comparison properties with explicit families of solutions of the corresponding equations. The primary ingredients of functions in these families are translates of solutions which depend radially on the space variables. Results of independent interest include the presentation and study of the class of infinity-caloric functions employed in the characterization.