G. Khuskivadze and V. Paatashvili

Zaremba'S Boundary Value Problem in the Smirnov Class of Harmonic Functions in Domains with Piecewise-Smooth Boundaries

abstract:
Zaremba's problem is studied in weighted Smirnov classes of harmonic functions in domains bounded by arbitrary simple smooth curves as well as in some domains with piecewise-smooth boundaries. The conditions of solvability are obtained and the solutions are written in quadratures.

Mathematics Subject Classification: 35J25, 31A05

Key words and phrases: Harmonic functions of Smirnov type, Zaremba's problem, mixed problem, weighted functions, Poisson integral, singular integral equation in a weight Lebesgue space