Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains: Volume II
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2000
|
| Schriftenreihe: | Operator Theory, Advances and Applications
112 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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, this second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this book 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 book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems |
| Beschreibung: | 1 Online-Ressource (XXIII, 323 p) |
| ISBN: | 9783034884327 9783034895644 |
| DOI: | 10.1007/978-3-0348-8432-7 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034884327 9783034895644 |
| language | English |
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| spelling | Maz’ya, Vladimir Verfasser aut Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II by Vladimir Maz’ya, Serguei Nazarov, Boris A. Plamenevskij Basel Birkhäuser Basel 2000 1 Online-Ressource (XXIII, 323 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory, Advances and Applications 112 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, this second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this book 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 book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems Mathematics Mathematics, general Mathematik Nazarov, Serguei Sonstige oth Plamenevskij, Boris A. Sonstige oth https://doi.org/10.1007/978-3-0348-8432-7 Verlag Volltext |
| spellingShingle | Maz’ya, Vladimir Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II Mathematics Mathematics, general Mathematik |
| title | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II |
| title_auth | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II |
| title_exact_search | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II |
| title_full | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II by Vladimir Maz’ya, Serguei Nazarov, Boris A. Plamenevskij |
| title_fullStr | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II by Vladimir Maz’ya, Serguei Nazarov, Boris A. Plamenevskij |
| title_full_unstemmed | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II by Vladimir Maz’ya, Serguei Nazarov, Boris A. Plamenevskij |
| title_short | Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains |
| title_sort | asymptotic theory of elliptic boundary value problems in singularly perturbed domains volume ii |
| title_sub | Volume II |
| topic | Mathematics Mathematics, general Mathematik |
| topic_facet | Mathematics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-0348-8432-7 |
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