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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Last modified: April 10, 2003