A Quasiconcavity Property for the Heat Equation in a Convex Ring

Jingjing Suo

doi:10.1007/s40304-020-00207-6

Communications in Mathematics and Statistics ›› 2020, Vol. 8 ›› Issue (4) : 453 -462. DOI: 10.1007/s40304-020-00207-6

Article

A Quasiconcavity Property for the Heat Equation in a Convex Ring

Jingjing Suo ¹^,^a

Author information +

History +

PDF

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

Cite this article

Download citation ▾

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