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Transactions of the American Mathematical Society

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


Authors: Eugene Fabes and Sandro Salsa
Journal: Trans. Amer. Math. Soc. 279 (1983), 635-650
MSC: Primary 35K05; Secondary 31C99
MathSciNet review: 709573
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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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DOI: https://doi.org/10.1090/S0002-9947-1983-0709573-7
Article copyright: © Copyright 1983 American Mathematical Society