FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 4, PAGES 1129-1158

On the mixed problem for Laplace equation outside cuts, placed along a circumference in a plane

A. I. Sgibnev
P. A. Krutitskii

Abstract

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The boundary value problem for harmonic functions outside cuts lying on the arcs of a circumference is considered. The Dirichlet condition is given on one side of each cut and Neumann condition is specified on the other side. The problem is reduced to the Riemann--Hilbert problem for complex analytic function, which is solved in a closed form. An explicit solution of the original problem is obtained.

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