Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary

Abstract

In the first part of the paper, the authors obtain the asymptotics of Green's function of the first boundary value problem for the heat equation in an m-dimensional cone K. The second part deals with the first boundary value problem for the heat equation in the domain K × R n–m . Here the right-hand side f of the heat equation is assumed to be an element of a weighted L p,q -space. The authors describe the behavior of the solution near the (n – m)-dimensional edge of the domain.