Crack Theory and Edge Singularities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2003
|
| Schriftenreihe: | Mathematics and Its Applications
561 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components |
| Beschreibung: | 1 Online-Ressource (XXVII, 485 p) |
| ISBN: | 9789401703239 9789048163847 |
| DOI: | 10.1007/978-94-017-0323-9 |
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| 500 | |a Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components | ||
| 650 | 4 | |a Mathematics | |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-0323-9 |
| format | Electronic eBook |
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| id | DE-604.BV042424198 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401703239 9789048163847 |
| language | English |
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| spelling | Kapanadze, David Verfasser aut Crack Theory and Edge Singularities by David Kapanadze, B.-Wolfgang Schulze Dordrecht Springer Netherlands 2003 1 Online-Ressource (XXVII, 485 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 561 Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components Mathematics Functional analysis Global analysis Operator theory Differential equations, partial Partial Differential Equations Operator Theory Global Analysis and Analysis on Manifolds Functional Analysis Applications of Mathematics Mathematik Schulze, B.-Wolfgang Sonstige oth https://doi.org/10.1007/978-94-017-0323-9 Verlag Volltext |
| spellingShingle | Kapanadze, David Crack Theory and Edge Singularities Mathematics Functional analysis Global analysis Operator theory Differential equations, partial Partial Differential Equations Operator Theory Global Analysis and Analysis on Manifolds Functional Analysis Applications of Mathematics Mathematik |
| title | Crack Theory and Edge Singularities |
| title_auth | Crack Theory and Edge Singularities |
| title_exact_search | Crack Theory and Edge Singularities |
| title_full | Crack Theory and Edge Singularities by David Kapanadze, B.-Wolfgang Schulze |
| title_fullStr | Crack Theory and Edge Singularities by David Kapanadze, B.-Wolfgang Schulze |
| title_full_unstemmed | Crack Theory and Edge Singularities by David Kapanadze, B.-Wolfgang Schulze |
| title_short | Crack Theory and Edge Singularities |
| title_sort | crack theory and edge singularities |
| topic | Mathematics Functional analysis Global analysis Operator theory Differential equations, partial Partial Differential Equations Operator Theory Global Analysis and Analysis on Manifolds Functional Analysis Applications of Mathematics Mathematik |
| topic_facet | Mathematics Functional analysis Global analysis Operator theory Differential equations, partial Partial Differential Equations Operator Theory Global Analysis and Analysis on Manifolds Functional Analysis Applications of Mathematics Mathematik |
| url | https://doi.org/10.1007/978-94-017-0323-9 |
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