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Table of contents (10 chapters)
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Front Matter
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Boundary Value Problems for the Laplace Operator in Domains Perturbed Near Isolated Singularities
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Front Matter
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General Elliptic Boundary Value Problems in Domains Perturbed Near Isolated Singularities of the Boundary
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Front Matter
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Asymptotic Behaviour of Functionals on Solutions of Boundary Value Problems in Domains Perturbed Near Isolated Boundary Singularities
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Front Matter
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Asymptotic Behaviour of Eigenvalues of Boundary Value Problems in Domains with Small Holes
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Front Matter
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Back Matter
About this book
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. This first volume is devoted to domains whose boundary is smooth in the neighborhood of finitely many conical points. In particular, the theory encompasses the important case of domains with small holes. The second volume, on the other hand, treats perturbations of the boundary in higher dimensions as well as nonlocal perturbations.
The core of this book consists of the solution of general elliptic boundary value problems by complete asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. The construction of this method capitalizes on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years.
Much attention is paid to concrete problems in mathematical physics, for example in elasticity theory. In particular, a study of the asymptotic behavior of stress intensity factors, energy integrals and eigenvalues is presented.
To a large extent the book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Authors and Affiliations
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Department of Mathematics, Linköping University, Linköping, Sweden
Vladimir Maz’ya
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Laboratory of Mathematical Methods in Mechanics of Solids Institute of Mathematics and Mechanics, St. Petersburg University, St. Petersburg, Russia
Serguei Nazarov
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Department of Mathematical Physics, Faculty of Physics, St. Petersburg State University, St. Petersburg, Russia
Boris A. Plamenevskij
Bibliographic Information
Book Title: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Book Subtitle: Volume I
Authors: Vladimir Maz’ya, Serguei Nazarov, Boris A. Plamenevskij
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-0348-8434-1
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkh�user Verlag 2000
Hardcover ISBN: 978-3-7643-6397-0Published: 01 May 2000
Softcover ISBN: 978-3-0348-9565-1Published: 21 October 2012
eBook ISBN: 978-3-0348-8434-1Published: 06 December 2012
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XXIII, 435
Additional Information: Original German edition published by Akademie Verlag Leipzig, 1991
Topics: Analysis