Geodesic
A gradient estimate for solutions of the heat equation. II
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 39-44.

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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.
Classification : 35B45, 35B50, 35B65, 35K05, 35K20
Keywords: gradient estimate; heat equation; maximum principle 
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     author = {Kahane, Charles S.},
     title = {A gradient estimate for solutions of the heat equation. {II}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {39--44},
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Kahane, Charles S. A gradient estimate for solutions of the heat equation. II. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 39-44. http://geodesic.mathdoc.fr/item/CMJ_2001__51_1_a3/