Monotonicity properties of the Neumann heat kernel in the ball |
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Authors: | Mihai N Pascu Maria E Gageonea |
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Institution: | Faculty of Mathematics and Computer Science, Transilvania University of Bra?ov, Bra?ov 500091, Romania |
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Abstract: | A well-known conjecture of R. Laugesen and C. Morpurgo asserts that the diagonal of the Neumann heat kernel of the unit ball U⊂Rn is a strictly increasing radial function. In this paper we use probabilistic arguments to settle this conjecture and to prove some inequalities for the Neumann heat kernel in the ball. |
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Keywords: | Neumann heat kernel Reflecting Brownian motion Hot Spots conjecture |
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