Boundary Integral Equations on Contours with Peaks

1 Lp -theory of boundary integral equations on a contour with peak.- 1.1 Introduction.- 1.2 Continuity of boundary integral operators.- 1.3 Dirichlet and Neumann problems for a domain with peak.- 1.4 Integral equations of the Dirichlet and Neumann problems.- 1.5 Direct method of integral equations of the Neumann and Dirichlet problems.- 2 Boundary integral equations in Hölder spaces on a contour with peak.- 2.1 Weighted Hölder spaces.- 2.2 Boundedness of integral operators.- 2.3 Dirichlet and Neumann problems in a strip.- 2.4 Boundary integral equations of the Dirichlet and Neumann problems in domains with outward peak.- 2.5 Boundary integral equations of the Dirichlet and Neumann problems in domains with inward peak.- 2.6 Integral equation of the first kind on a contour with peak.- 2.7 Appendices.- 3 Asymptotic formulae for solutions of boundary integral equations near peaks.- 3.1 Preliminary facts.- 3.2 The Dirichlet and Neumann problems for domains with peaks.- 3.3 Integral equations of the Dirichlet problem.- 3.4 Integral equations of the Neumann problem.- 3.5 Appendices.- 4 Integral equations of plane elasticity in domains with peak.- 4.1 Introduction.- 4.2 Boundary value problems of elasticity.- 4.3 Integral equations on a contour with inward peak.- 4.4 Integral equations on a contour with outward peak.- Bibliography.