Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders
Eugene B. Fabes, Sandro Salsa · Transactions of the American Mathematical Society · 1983
In this paper the authors prove unique solvability of the initial-Dirichlet problem for the heat equation in a cylindrical domain with Lipschitz base, lateral data in L p , p ⩾ 2 {L^p},p \geqslant 2 , and zero initial values. A Poisson kernel for this problem is shown to exist with the property that its L 2 {L^2} -averages over parabolic rectangles are equivalent to L 1 {L^1} -averages over the same sets.