Elliptic partial differential equations and quasiconformal mappings in the plane:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2009]
|
| Schriftenreihe: | Princeton mathematical series
48 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1515/9781400830114?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400830114&searchTitles=true https://doi.org/10.1515/9781400830114 |
| Beschreibung: | Main description: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings |
| Umfang: | 1 Online-Ressource (XVI, 677 S.) |
| ISBN: | 9781400830114 |
| DOI: | 10.1515/9781400830114 |
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| institution | BVB |
| isbn | 9781400830114 |
| language | English |
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| spelling | Astala, Kari 1953- Verfasser (DE-588)137232969 aut Elliptic partial differential equations and quasiconformal mappings in the plane Kari Astala, Tadeusz Iwaniec, and Gaven Martin Princeton, N.J. Princeton University Press [2009] © 2009 1 Online-Ressource (XVI, 677 S.) txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series 48 Main description: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings Differential equations, Elliptic Quasiconformal mappings Quasikonforme Abbildung (DE-588)4199279-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Quasikonforme Abbildung (DE-588)4199279-9 s DE-604 Iwaniec, Tadeusz 1947- Verfasser (DE-588)1024208818 aut Martin, Gaven Verfasser aut Erscheint auch als Druck-Ausgabe 978-0-691-13777-3 Princeton mathematical series 48 (DE-604)BV045898993 48 http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400830114&searchTitles=true Verlag Volltext https://doi.org/10.1515/9781400830114 Verlag Volltext |
| spellingShingle | Astala, Kari 1953- Iwaniec, Tadeusz 1947- Martin, Gaven Elliptic partial differential equations and quasiconformal mappings in the plane Princeton mathematical series Differential equations, Elliptic Quasiconformal mappings Quasikonforme Abbildung (DE-588)4199279-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4199279-9 (DE-588)4014485-9 |
| title | Elliptic partial differential equations and quasiconformal mappings in the plane |
| title_auth | Elliptic partial differential equations and quasiconformal mappings in the plane |
| title_exact_search | Elliptic partial differential equations and quasiconformal mappings in the plane |
| title_full | Elliptic partial differential equations and quasiconformal mappings in the plane Kari Astala, Tadeusz Iwaniec, and Gaven Martin |
| title_fullStr | Elliptic partial differential equations and quasiconformal mappings in the plane Kari Astala, Tadeusz Iwaniec, and Gaven Martin |
| title_full_unstemmed | Elliptic partial differential equations and quasiconformal mappings in the plane Kari Astala, Tadeusz Iwaniec, and Gaven Martin |
| title_short | Elliptic partial differential equations and quasiconformal mappings in the plane |
| title_sort | elliptic partial differential equations and quasiconformal mappings in the plane |
| topic | Differential equations, Elliptic Quasiconformal mappings Quasikonforme Abbildung (DE-588)4199279-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Differential equations, Elliptic Quasiconformal mappings Quasikonforme Abbildung Elliptische Differentialgleichung |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400830114&searchTitles=true https://doi.org/10.1515/9781400830114 |
| volume_link | (DE-604)BV045898993 |
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