Brownian motion with killing and reflection and the "hot--spots" problem

Rodrigo Banuelos, Michael Pang, Mihai Pascu

Published 2004-07-16Version 1

We investigate the "hot--spots" property for the survival time probability of Brownian motion with killing and reflection in planar convex domains whose boundary consists of two curves, one of which is an arc of a circle, intersecting at acute angles. This leads to the "hot--spots" property for the mixed Dirichlet--Neumann eigenvalue problem in the domain with Neumann conditions on one of the curves and Dirichlet conditions on the other