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Keywords:
gradient estimate; heat equation; maximum principle
gradient estimate; heat equation; maximum principle
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.
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References:
[1] C. Kahane: A gradient estimate for solutions of the heat equation. Czechoslovak Math. J. 48(123) (1998), 711–725. DOI 10.1023/A:1022487622757 | MR 1658249 | Zbl 0951.35017
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