Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 35, No 4, (2009), 317p-342p
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.