Probabilistic Approach to the Neumann Problem for a Symmetric Operator

Benchérif-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 -