Sobolev Gradients and Differential Equations (Lecture Notes in Mathematics)

Neuberger, John

ISBN 10: 3540635378 / ISBN 13: 9783540635376

Published by Springer, 1997

About this Item

X_Library copy with minimal use. No text marks.

Seller Inventory # 26070397

Bibliographic Details

• Title: Sobolev Gradients and Differential Equations (Lecture Notes in Mathematics)
• Publisher: Springer
• Publication Date: 1997
• Language: English
• ISBN 10: 3540635378
• ISBN 13: 9783540635376
• Binding: Paperback
• Condition: Good
• Weight: 9 ounces

About this title

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.