Asymptotic expansions for anisotropic heat kernels

Abstract

We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two in some variables but higher in the other ones. In the second one, we consider the heat equation on the Heisenberg group.