On a class of conditionally solvable nonlocal boundary value problems for harmonic functions. (English. Russian original) Zbl 0607.30039

Sov. Math., Dokl. 31, 91-94 (1985); translation from Dokl. Akad. Nauk SSSR 280, 521-524 (1985).
In the complex plane let \(S_ 1\) and \(S_ 2\) be two closed Jordan curves and \(t_ 2=\gamma (t_ 1)\), \(t_ 1\in S_ 1\), \(t_ 2\in S_ 2\) a homeomorphism between \(S_ 1\) and \(S_ 2\). Find a harmonic function u(z) satisfyng the boundary condition \(u(t)-u(\gamma (t))=f(t)\), \(t\in S_ 1\). The condition for the solvability of this problem is investigated. Some examples are considered.
Reviewer: M.Schleiff


30E25 Boundary value problems in the complex plane
31A25 Boundary value and inverse problems for harmonic functions in two dimensions