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Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders

Eugene Fabes, Sandro Salsa
1983 Transactions of the American Mathematical Society  
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