Boundary integral equations on contours with peaks / Vladimir G. Maz'ya, Alexander A. Soloviev ; translated into English and edited by Tatyana Shaposhnikova
Lp-theory of Boundary Integral Equations on a Contour with Peak -- Boundary Integral Equations in Hölder Spaces on a Contour with Peak -- Asymptotic Formulae for Solutions of Boundary Integral Equations Near Peaks -- Integral Equations of Plane Elasticity in Domains with Peak
Summary
The purpose of this book is to give a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. The theory was developed by the authors during the last twenty years and the present volume is based on their results. The first three chapters are devoted to harmonic potentials, and in the final chapter elastic potentials are treated. Theorems on solvability in various function spaces and asymptotic representations for solutions near the cusps are obtained. Kernels and cokernels of the integral operators are explicitly described. The method is based on a study of auxiliary boundary value problems which is of interest in itself
