EQUATION IN LIPSCHITZ CYLINDERS
R. M. Brown · 2016
1. Introduction. In this paper, we study the initial-Neumann and the initial-Dirichlet problems for the heat equation in Lipschitz cylinders. We consider each of these problems when the lateral data lies inL2 and the initial data is zero. We also consider regularity of solutions to the initialDirichlet problem when the lateral data lies in a Sobolev space of functions with one spatial derivative and half of a time derivative in L2. Existence of our solutions is established by the classical method of layer potentials.