On some integrals on a surface with a conical point (Q2459774)

The main purpose of the present paper is to generalize the integral equation method to boundary value problems on surfaces with a conical point. The author first studies various properties of some integrals occuring in the analysis of boundary value problems in the framework of a surface with a conical point. Next, integral equations containing kernels of a classical double layer potential and the normal derivative of a simple layer potential are considered. A Fredholm alternative for such equations is established. Applications to Dirichlet and Neumann boundary value problems are also provided as illustrations of the abstract results established in this paper.