Sobolev Gradients and Differential Equations

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 numer...

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Main Author: neuberger, john
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1997, 1997
Edition:1st ed. 1997
Series:Lecture Notes in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Summary: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
Physical Description:VIII, 152 p online resource
ISBN:9783540695943