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Killed Brownian motion and the Brunn–Minkowski inequalities

Published online by Cambridge University Press:  22 February 2012

HUILING LE
HUILING LE*
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD. e-mail: [email protected]
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Abstract

We construct triplets of killed Brownian motions to obtain the Brunn–Minkowski inequalities concerning the solutions of the equation (1/2)Δψ − h ψ = g on three interrelated compact sets in Euclidean space. These, in particular, include inequalities relating to the solutions of the Schrödinger equation and the Poisson equation on the three compact convex sets and an inequality relating to harmonic functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 1 , July 2012 , pp. 111 - 121
Copyright
Copyright © Cambridge Philosophical Society 2012

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