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

Mathematics – Probability

Scientific paper

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Scientific paper

10.1007/s00440-003-0323-x

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

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