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Title: Probabilistic Approach to the Neumann Problem for a Symmetric Operator
Authors: Benchérif-Madani, Abdelatif
Keywords: Neumann and Steklov Problems
Exponential Ergodicity
Double Layer Potential
Reflecting Diffusion
Lipschitz Domain
Issue Date: 2009
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 4, (2009), 317p-342p
Abstract: We give a probabilistic formula for the solution of a non-homogeneous Neumann problem for a symmetric nondegenerate operator of second order in a bounded domain. We begin with a g-Hölder matrix and a C^1,g domain, g > 0, and then consider extensions. The solutions are expressed as a double layer potential instead of a single layer potential; in particular a new boundary function is discovered and boundary random walk methods can be used for simulations. We use tools from harmonic analysis and probability theory.
Description: 2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.
ISSN: 1310-6600
Appears in Collections:Volume 35, Number 4

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