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A gradient estimate for solutions of the heat equation. II. (English) Zbl 1079.35037
Summary: The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
Part I, cf. ibid. 48, No.4, 711-725 (1998; Zbl 0951.35017)..

35K05 Heat equation
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[1] C. Kahane: A gradient estimate for solutions of the heat equation. Czechoslovak Math. J. 48(123) (1998), 711-725. · Zbl 0951.35017
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