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Killed Brownian motion and the Brunn–Minkowski inequalities
Published online by Cambridge University Press: 22 February 2012
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