Removable singularities for Lipschitz caloric functions in time varying domains

Abstract

In this paper we study removable singularities for regular $(1,1/2)$-Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric capacity and we study its metric and geometric properties and the connection with the $L^2$ boundedness of the singular integral whose kernel is given by the gradient of the fundamental solution of the heat equation.