Boundary Integral Equations in Hölder Spaces on a Contour with Peak
Vladimir Gilelevich Maz'ya, Alexander A. Soloviev · Birkhäuser Basel eBooks · 2010
In this chapter we are concerned with the solvability in Hölder spaces and description of kernels of boundary integral equations of the Dirichlet problem (2.1) $$ \Delta u = 0 in \Omega ^ + , u| _\Gamma = \phi , $$ and the Neumann problem (2.2) $$ \Delta u = 0 in \Omega ^ + , (\partial u/\partial n)| _\Gamma = \psi , $$ 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.