A Probabilistic Formula for a Poisson Equation with Neumann Boundary Condition

DOI10.1080/07362990902976520zbMath1171.35493OpenAlexW2020424615MaRDI QIDQ3391778

Etienne Pardoux, Abdellatif Benchérif-Madani

Publication date: 13 August 2009

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990902976520

zbMATH Keywords

Neumann boundary conditionprobabilistic approachreflection diffusionelliptical Poisson equation

Mathematics Subject Classification ID

Diffusion processes (60J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

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• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: A probabilistic approach
• Large time behavior of solutions to parabolic equations with Neumann boundary conditions
• Stochastic differential equations with reflecting boundary conditions
• A probalistic solution of the Neumann problem.

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