Sobolev Gradients and Differential Equations: v. 1670 (Lecture Notes in Mathematics) - Softcover

Neuberger, John W.

Softcover

ISBN 10: 3540635378 ISBN 13: 9783540635376

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1997

Synopsis

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.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1997
• Language: English
• ISBN 10: 3540635378
• ISBN 13: 9783540635376
• Binding: Paperback
• Number of pages: 158