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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 Lp, p > 2, and zero initial values. A Poisson kernel for this problem is shown to exist with the property that its L2-averages over parabolic rectangles are equivalent to ¿'-averages over the same sets.doi:10.1090/s0002-9947-1983-0709573-7 fatcat:2knldcdqdrgvrnabiizimctf4y