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Sobolev Gradients and Differential Equations

Produktform: E-Buch Text Elektronisches Buch in proprietärem

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.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-3-540-69594-3 / 978-3540695943 / 9783540695943

Verlag: Springer Berlin

Erscheinungsdatum: 13.11.2006

Seiten: 152

Autor(en): John Neuberger

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