Caloric function

Summary

A caloric function is a solution of the heat equation $\partial_t u = \Delta u$ on an open set of space-time. Caloric functions play for the heat equation the role that harmonic functions play for the Laplace equation. Much of classical potential theory, such as mean value formulas, maximum principles and the Perron method, has a parallel version for caloric functions. This parallel theory is often called parabolic or caloric potential theory.