FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 6, PAGES 115-135

The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane

P. A. Krutitskii
A. I. Sgibnev

Abstract

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We consider the mixed problem for Laplace's equation outside cuts in a plane. The Dirichlet boundary condition is posed on one side of each cut, and the skew derivative condition is posed on the other side. This problem generalizes the mixed Dirichlet--Neumann problem. Using the method of potentials, this problem is reduced to a uniquely solvable Fredholm integral equation of the second kind.

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Last modified: February 26, 2007