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

Eugene Fabes, Sandro Salsa
<span title="1983-02-01">1983</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1090/s0002-9947-1983-0709573-7</a> <a target="_blank" rel="external noopener" href="">fatcat:2knldcdqdrgvrnabiizimctf4y</a> </span>
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