A Quasiconcavity Property for the Heat Equation in a Convex Ring

Jingjing Suo

Communications in Mathematics and Statistics ›› 2020, Vol. 8 ›› Issue (4) : 453 -462.

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Communications in Mathematics and Statistics ›› 2020, Vol. 8 ›› Issue (4) : 453 -462. DOI: 10.1007/s40304-020-00207-6
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A Quasiconcavity Property for the Heat Equation in a Convex Ring

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Abstract

We give an exposition of a result of Borell (Commun Math Phys 86:143–147, 1982) that the probability function that Brownian motion hits the inner boundary before time t and before hitting the outer boundary is a space-time quasiconcave function.

Keywords

Heat equation / Quasiconcavity / Maximum principle / Comparison method

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Jingjing Suo. A Quasiconcavity Property for the Heat Equation in a Convex Ring. Communications in Mathematics and Statistics, 2020, 8(4): 453-462 DOI:10.1007/s40304-020-00207-6

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Funding

Chinese Government Scholarship(201606340046)

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