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Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders
<span title="1983-02-01">1983</span>
<i title="American Mathematical Society (AMS)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a>
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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.
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