Sobolev Gradients and Differential Equations
Seiten
1997
Springer Berlin (Hersteller)
978-3-540-63537-6 (ISBN)
Springer Berlin (Hersteller)
978-3-540-63537-6 (ISBN)
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A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
| Reihe/Serie | Lecture Notes in Mathematics ; 1670 |
|---|---|
| Sprache | englisch |
| Gewicht | 245 g |
| Einbandart | Paperback |
| Schlagworte | Differenzialgleichungen |
| ISBN-10 | 3-540-63537-8 / 3540635378 |
| ISBN-13 | 978-3-540-63537-6 / 9783540635376 |
| Zustand | Neuware |
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