Brownian motion with killing and reflection and the "hot--spots" problem
arXiv:math/0407297 · doi:10.1007/s00440-003-0323-x
Abstract
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