Killed Brownian motion and the Brunn–Minkowski inequalities

Killed Brownian motion and the Brunn–Minkowski inequalities

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 equati...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2012-07, Vol.153 (1), p.111-121
1. Verfasser: LE, HUILING
Format: Artikel
Sprache:eng
Schlagworte:
Brownian motion
Construction
Geometry
Harmonic functions
Inequalities
Mathematical analysis
Poisson equation
Schroedinger equation
Theorems
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004112000060