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Partial Differential Equations VI: Elliptic and Parabolic Operators (Encyclopaedia of Mathematical Sciences) - Softcover

 
9783642081170: Partial Differential Equations VI: Elliptic and Parabolic Operators (Encyclopaedia of Mathematical Sciences)

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Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject.

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  • PublisherSpringer
  • Publication date2010
  • ISBN 10 3642081177
  • ISBN 13 9783642081170
  • BindingPaperback
  • LanguageEnglish
  • Number of pages332
  • EditorEgorov Yu.V., Shubin M.A.

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9783540546788: Partial Differential Equations VI: Elliptic and Parabolic Operators (Encyclopaedia of Mathematical Sciences, 63)

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ISBN 10:  3540546782 ISBN 13:  9783540546788
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 340 pp. Englisch. Seller Inventory # 9783642081170

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783642081170

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Egorov, Yu.V.|Shubin, Mikhail A.|Agranovich, M. S.|Ejdel\'man, S. D.|Levendorskij, S. Z.|Paneah, B.
Published by Springer Berlin Heidelberg, 2010
ISBN 10: 3642081177 ISBN 13: 9783642081170
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researcher. Seller Inventory # 5047164

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