Brownian motion with killing and reflection and the ‘‘hot–spots’’ problem

2004/03/03 by Rodrigo Bañuelos, Rodrigo Banuelos, Michael Pang +2 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #math.AP #math.PR

paper · pdf · doi:10.1007/s00440-003-0323-x

published as Probab. Theory Relat. Fields 130, 56-68 (2004)

openalex publication_date 2004/03/03 · arxiv created 2004/07/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Cited by

• Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

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