Partial Differential Equations VI: Elliptic and Parabolic Operators
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Series: | Encyclopaedia of Mathematical Sciences
63 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 0. 1. The Scope of the Paper. This article is mainly devoted to the oper ators indicated in the title. More specifically, we consider elliptic differential and pseudodifferential operators with infinitely smooth symbols on infinitely smooth closed manifolds, i. e. compact manifolds without boundary. We also touch upon some variants of the theory of elliptic operators in !Rn. A separate article (Agranovich 1993) will be devoted to elliptic boundary problems for elliptic partial differential equations and systems. We now list the main topics discussed in the article. First of all, we ex pound theorems on Fredholm property of elliptic operators, on smoothness of solutions of elliptic equations, and, in the case of ellipticity with a parame ter, on their unique solvability. A parametrix for an elliptic operator A (and A-). . J) is constructed by means of the calculus of pseudodifferential also for operators in !Rn, which is first outlined in a simple case with uniform in x estimates of the symbols. As functional spaces we mainly use Sobolev £ - 2 spaces. We consider functions of elliptic operators and in more detail some simple functions and the properties of their kernels. This forms a foundation to discuss spectral properties of elliptic operators which we try to do in maxi mal generality, i. e. , in general, without assuming selfadjointness. This requires presenting some notions and theorems of the theory of nonselfadjoint linear operators in abstract Hilbert space |
| Physical Description: | 1 Online-Ressource (VII, 325 p) |
| ISBN: | 9783662092095 9783642081170 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-09209-5 |
Staff View
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662092095 9783642081170 |
| issn | 0938-0396 |
| language | English |
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| publishDate | 1994 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Egorov, Yu. V. Verfasser aut Partial Differential Equations VI Elliptic and Parabolic Operators edited by Yu. V. Egorov, M. A. Shubin Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (VII, 325 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 63 0938-0396 0. 1. The Scope of the Paper. This article is mainly devoted to the oper ators indicated in the title. More specifically, we consider elliptic differential and pseudodifferential operators with infinitely smooth symbols on infinitely smooth closed manifolds, i. e. compact manifolds without boundary. We also touch upon some variants of the theory of elliptic operators in !Rn. A separate article (Agranovich 1993) will be devoted to elliptic boundary problems for elliptic partial differential equations and systems. We now list the main topics discussed in the article. First of all, we ex pound theorems on Fredholm property of elliptic operators, on smoothness of solutions of elliptic equations, and, in the case of ellipticity with a parame ter, on their unique solvability. A parametrix for an elliptic operator A (and A-). . J) is constructed by means of the calculus of pseudodifferential also for operators in !Rn, which is first outlined in a simple case with uniform in x estimates of the symbols. As functional spaces we mainly use Sobolev £ - 2 spaces. We consider functions of elliptic operators and in more detail some simple functions and the properties of their kernels. This forms a foundation to discuss spectral properties of elliptic operators which we try to do in maxi mal generality, i. e. , in general, without assuming selfadjointness. This requires presenting some notions and theorems of the theory of nonselfadjoint linear operators in abstract Hilbert space Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Shubin, M. A. Sonstige oth https://doi.org/10.1007/978-3-662-09209-5 Verlag Volltext |
| spellingShingle | Egorov, Yu. V. Partial Differential Equations VI Elliptic and Parabolic Operators Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| title | Partial Differential Equations VI Elliptic and Parabolic Operators |
| title_auth | Partial Differential Equations VI Elliptic and Parabolic Operators |
| title_exact_search | Partial Differential Equations VI Elliptic and Parabolic Operators |
| title_full | Partial Differential Equations VI Elliptic and Parabolic Operators edited by Yu. V. Egorov, M. A. Shubin |
| title_fullStr | Partial Differential Equations VI Elliptic and Parabolic Operators edited by Yu. V. Egorov, M. A. Shubin |
| title_full_unstemmed | Partial Differential Equations VI Elliptic and Parabolic Operators edited by Yu. V. Egorov, M. A. Shubin |
| title_short | Partial Differential Equations VI |
| title_sort | partial differential equations vi elliptic and parabolic operators |
| title_sub | Elliptic and Parabolic Operators |
| topic | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-3-662-09209-5 |
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