# Boundary Integral Equations on Contours with Peaks

## byVladimir Maz'ya, Alexander Soloviev

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This book is a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. Three chapters cover harmonic potentials, and the final chapter treats elastic potentials.

Title:Boundary Integral Equations on Contours with PeaksFormat:HardcoverDimensions:344 pagesPublished:November 19, 2009Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034601700

ISBN - 13:9783034601702

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Table of Contents

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.