John Neuberger

Sobolev Gradients and Differential Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 152
• Erscheinungstermin: 13. November 2006
• Englisch
• ISBN-13: 9783540695943
• Artikelnr.: 53206147