a1 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD. e-mail: email@example.com
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.
(Received January 11 2011)
(Revised October 26 2011)
(Online publication February 22 2012)