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Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

SET

  • Book
  • © 2000

Overview

Authors:
  1. Vladimir Maz'ya

    1. Linköping University Department of Mathematics, Linköping, Sweden

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  2. Serguei Nazarov
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  3. Boris Plamenevskij
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Part of the book series: Operator Theory: Advances and Applications (OT, volume 111/112)

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Keywords

  • Partial differential equations

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. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work 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

  • Linköping University Department of Mathematics, Linköping, Sweden

    Vladimir Maz'ya

Bibliographic Information

  • Book Title: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

  • Book Subtitle: SET

  • Authors: Vladimir Maz'ya, Serguei Nazarov, Boris Plamenevskij

  • Series Title: Operator Theory: Advances and Applications

  • Publisher: Birkhäuser Basel

  • Copyright Information: Birkhäuser Basel 2000

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XLII, 758

  • Additional Information: Original German edition published by Akademie Verlag Leipzig, 1991

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