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The probabilistic solution of the third boundary value problem for second order elliptic equations

Authors:

Vassilis G. Papanicolaou

Affiliation:

1. Department of Mathematics, Duke University, 27706, Durham, NC, USA

Abstract:

Using standard reflected Brownian motion (SRBM) and martingales we define (in the spirit of Stroock and Varadhan-see [S-V]) the probabilistic solution of the boundary value problem

$begin{gathered} frac{1}{2}Delta u + qu = 0, in D; hfill frac{{partial u}}{{partial n}} + cu = - f,onpartial D, hfill end{gathered}$

Keywords:
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