V. Kokilashvili and V. Paatashvili

Neumann Problem in a Class of Harmonic Functions in Domains with a Piecewise-Lyapunov Boundary

The Neumann boundary value problem is considered in a finite simply connected domain $D$ with piecewise Lyapunov boundary free from zero interior angles. The solution is sought in the class of harmonic functions $u$ satisfying $(1)$, where $\Gm_r$ is the image of the circle $|z|=r$ under the conform mapping of the unit disc onto $D$.

Mathematics Subject Classification: 35J25, 35J40, 35B65.

Key words and phrases: Dirichlet and Neumann problem, Smirnov class, conformal mapping, piecewise Lyapunov boundary, two-weight inequality, Cauchy type integral.