Geodesic
Probabilistic Approach to the Neumann Problem for a Symmetric Operator
Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 317-342.

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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.
Keywords: Neumann and Steklov Problems, Exponential Ergodicity, Double Layer Potential, Reflecting Diffusion, Lipschitz Domain 
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Benchérif-Madani, Abdelatif. Probabilistic Approach to the Neumann Problem for a Symmetric Operator. Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 317-342. http://geodesic.mathdoc.fr/item/SMJ2_2009_35_4_a0/