Boundary Integral Equations in Hölder Spaces on a Contour with Peak

Abstract

In this chapter we are concerned with the solvability in Hölder spaces and description of kernels of boundary integral equations of the Dirichlet problem

$$ \Delta u = 0 in \Omega ^ + , u| _\Gamma = \phi , $$

((2.1))

and the Neumann problem

$$ \Delta u = 0 in \Omega ^ + , (\partial u/\partial n)| _\Gamma = \psi , $$

((2.2))

in a plane bounded simply connected domain Ω⁺ with a peak at the boundary Γ. Here and elsewhere we assume the normal n to be outward. Another assumption is that the vertex of the peak is placed at the origin.