V. Kokilashvili, V. Paatashvili

The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes

abstract:
We investigate the Dirichlet problem in domains with nonsmooth boundaries when a boundary function belongs to functional classes of the Zygmund class type. A complete picture of solvability is established also in the case of existence of solutions for which explicit expressions are found.