The Oblique Derivative Problem for the Laplace Equation in a Plain Domain

The oblique derivative problem for the Laplace equation is studied in a planar multiply connected domain. The boundary condition has a form where is the unit normal vector, is the unit tangential vector and is a fixed real number. If is a Hölderian function and the corresponding domain has Ljapunov boundary then the classical problem is studied. If on the boundary and the domain has a locally Lipschitz boundary then a solution, which fulfils the boundary condition in the sense of a nontangential limit, is studied. If is a real measure on the boundary and the domain has bounded cyclic variation then a solution in a sense of distributions is studied. The solution is looked for in a form of a linear combination of a single layer potential and an angular potential.