Pseudodifferential Operators and Nonlinear PDE:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1991
|
| Schriftenreihe: | Progress in Mathematics
100 |
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBT01 Volltext |
| Beschreibung: | For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. One goal has been to build a bridge between two approaches which have been used in a number of papers written in the last decade, one being the theory of paradifferential operators, pioneered by Bony and Meyer, the other the study of pseudodifferential operators whose symbols have limited regularity. The latter approach is a natural successor to classical devices of deriving estimates for linear PDE whose coefficients have limited regularity in order to obtain results in nonlinear PDE. After developing the requisite tools, we proceed to demonstrate their effectiveness on a range of basic topics in nonlinear PDE. For example, for hyperbolic systems, known sufficient conditions for persistence of solutions are both sharpened and extended in scope. In the treatment of parabolic equations and elliptic boundary problems, it is shown that the results obtained here interface particularly easily with the DeGiorgi-Nash-Moser theory, when that theory applies. To make the work reasonable self-contained, there are appendices treating background topics in harmonic analysis and the DeGiorgi-Nash-Moser theory, as well as an introductory chapter on pseudodifferential operators as developed for linear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis |
| Beschreibung: | 1 Online-Ressource (228p) |
| ISBN: | 9781461204312 |
| DOI: | 10.1007/978-1-4612-0431-2 |
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| 500 | |a For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. One goal has been to build a bridge between two approaches which have been used in a number of papers written in the last decade, one being the theory of paradifferential operators, pioneered by Bony and Meyer, the other the study of pseudodifferential operators whose symbols have limited regularity. The latter approach is a natural successor to classical devices of deriving estimates for linear PDE whose coefficients have limited regularity in order to obtain results in nonlinear PDE. After developing the requisite tools, we proceed to demonstrate their effectiveness on a range of basic topics in nonlinear PDE. For example, for hyperbolic systems, known sufficient conditions for persistence of solutions are both sharpened and extended in scope. In the treatment of parabolic equations and elliptic boundary problems, it is shown that the results obtained here interface particularly easily with the DeGiorgi-Nash-Moser theory, when that theory applies. To make the work reasonable self-contained, there are appendices treating background topics in harmonic analysis and the DeGiorgi-Nash-Moser theory, as well as an introductory chapter on pseudodifferential operators as developed for linear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis | ||
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Datensatz im Suchindex
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| author | Taylor, Michael E. |
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| author_variant | m e t me met |
| building | Verbundindex |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0431-2 |
| format | Electronic eBook |
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| language | English |
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| spelling | Taylor, Michael E. Verfasser aut Pseudodifferential Operators and Nonlinear PDE by Michael E. Taylor Boston, MA Birkhäuser Boston 1991 1 Online-Ressource (228p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 100 For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. One goal has been to build a bridge between two approaches which have been used in a number of papers written in the last decade, one being the theory of paradifferential operators, pioneered by Bony and Meyer, the other the study of pseudodifferential operators whose symbols have limited regularity. The latter approach is a natural successor to classical devices of deriving estimates for linear PDE whose coefficients have limited regularity in order to obtain results in nonlinear PDE. After developing the requisite tools, we proceed to demonstrate their effectiveness on a range of basic topics in nonlinear PDE. For example, for hyperbolic systems, known sufficient conditions for persistence of solutions are both sharpened and extended in scope. In the treatment of parabolic equations and elliptic boundary problems, it is shown that the results obtained here interface particularly easily with the DeGiorgi-Nash-Moser theory, when that theory applies. To make the work reasonable self-contained, there are appendices treating background topics in harmonic analysis and the DeGiorgi-Nash-Moser theory, as well as an introductory chapter on pseudodifferential operators as developed for linear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis Mathematics Global analysis (Mathematics) Operator theory Differential equations, partial Partial Differential Equations Operator Theory Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Pseudodifferentialoperator (DE-588)4047640-6 s 1\p DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s 2\p DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 3\p DE-604 Erscheint auch als Druckausgabe 978-0-8176-3595-4 https://doi.org/10.1007/978-1-4612-0431-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Taylor, Michael E. Pseudodifferential Operators and Nonlinear PDE Mathematics Global analysis (Mathematics) Operator theory Differential equations, partial Partial Differential Equations Operator Theory Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4205536-2 (DE-588)4128900-6 (DE-588)4047640-6 |
| title | Pseudodifferential Operators and Nonlinear PDE |
| title_auth | Pseudodifferential Operators and Nonlinear PDE |
| title_exact_search | Pseudodifferential Operators and Nonlinear PDE |
| title_full | Pseudodifferential Operators and Nonlinear PDE by Michael E. Taylor |
| title_fullStr | Pseudodifferential Operators and Nonlinear PDE by Michael E. Taylor |
| title_full_unstemmed | Pseudodifferential Operators and Nonlinear PDE by Michael E. Taylor |
| title_short | Pseudodifferential Operators and Nonlinear PDE |
| title_sort | pseudodifferential operators and nonlinear pde |
| topic | Mathematics Global analysis (Mathematics) Operator theory Differential equations, partial Partial Differential Equations Operator Theory Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Operator theory Differential equations, partial Partial Differential Equations Operator Theory Analysis Mathematik Partielle Differentialgleichung Nichtlineare Differentialgleichung Nichtlineare partielle Differentialgleichung Pseudodifferentialoperator |
| url | https://doi.org/10.1007/978-1-4612-0431-2 |
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