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

Fabes, Eugene; Salsa, Sandro

doi:10.1090/S0002-9947-1983-0709573-7

Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders
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by Eugene Fabes and Sandro Salsa PDF

Trans. Amer. Math. Soc. 279 (1983), 635-650 Request permission

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 ${L^p},p \geqslant 2$, and zero initial values. A Poisson kernel for this problem is shown to exist with the property that its ${L^2}$-averages over parabolic rectangles are equivalent to ${L^1}$-averages over the same sets.

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