# Probabilistic Approach to the Neumann Problem for a Symmetric Operator

Serdica Mathematical Journal (2009)

- Volume: 35, Issue: 4, page 317-342
- ISSN: 1310-6600

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topBenchérif-Madani, Abdelatif. "Probabilistic Approach to the Neumann Problem for a Symmetric Operator." Serdica Mathematical Journal 35.4 (2009): 317-342. <http://eudml.org/doc/281439>.

@article{Benchérif2009,

abstract = {2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.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.},

author = {Benchérif-Madani, Abdelatif},

journal = {Serdica Mathematical Journal},

keywords = {Neumann and Steklov Problems; Exponential Ergodicity; Double Layer Potential; Reflecting Diffusion; Lipschitz Domain; Neumann and Steklov problems; exponential ergodicity; double layer potential; reflecting diffusion; Lipschitz domain},

language = {eng},

number = {4},

pages = {317-342},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Probabilistic Approach to the Neumann Problem for a Symmetric Operator},

url = {http://eudml.org/doc/281439},

volume = {35},

year = {2009},

}

TY - JOUR

AU - Benchérif-Madani, Abdelatif

TI - Probabilistic Approach to the Neumann Problem for a Symmetric Operator

JO - Serdica Mathematical Journal

PY - 2009

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 35

IS - 4

SP - 317

EP - 342

AB - 2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.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.

LA - eng

KW - Neumann and Steklov Problems; Exponential Ergodicity; Double Layer Potential; Reflecting Diffusion; Lipschitz Domain; Neumann and Steklov problems; exponential ergodicity; double layer potential; reflecting diffusion; Lipschitz domain

UR - http://eudml.org/doc/281439

ER -

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