Abstract
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.
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