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Short Communications

Some Generalizations of the Boundary Value Problem with Oblique Derivative

A. L. Rozental'

Moscow

Abstract: Let $D$ be a two-dimensional domain bounded by a smooth closed contour $L$ and let $l$ be a smooth vector field on $L\setminus\Gamma$ where $\Gamma$ is finite. Using probability methods we investigate the bounded solutions of the boundary value problem $\Delta u=0$, $\frac{\partial u}{\partial l}\bigg|_{L\setminus\Gamma}=0$ and prove that they may be uniquely represented in form (2).

Received: 10.09.1966

 English version: Theory of Probability and its Applications, 1967, 12:2, 329–333

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