Analysis IV: Linear and Boundary Integral Equations (Encyclopaedia of Mathematical Sciences)

Maz'ya, V.G. [Editor]; Nikol'skii, S.M. [Editor]; Böttcher, Albrecht [Translator]; Prössdorf, Siegfried [Translator];

ISBN 10: 3540519971 / ISBN 13: 9783540519973

Editore: Springer, 1991

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Dati bibliografici

• Titolo: Analysis IV: Linear and Boundary Integral Equations (Encyclopaedia of Mathematical Sciences)
• Editore: Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540519971
• ISBN 13: 9783540519973
• Rilegatura: Hardcover
• Condizione: New

Descrizione articolo

Riassunto

The first part of this volume is a survey of the current state of the theory of linear integral equations. Material from abstract operator theory is presented first, before moving on to a detailed discussion of Fredholm operators and estimates for the eigenvalues and singular numbers of integral operators. Other sections of this part are devoted to the theories of one-, and higher-dimensional singular operators. The second part of the volume concentrates on theoretical aspects of the boundary integral equation method, with particular emphasis on the results for equations on non-smooth surfaces obtained during the last few years. A survey of the classical theory of harmonic potentials and the boundary integral equations on smooth surfaces generated by such potentials is given and the theory is then extended to elastic and hydrodynamic potentials and to other problems of mathematical physics, including the oblique derivative problem, the biharmonic equation, the heat and wave equations and viscoelasticity.