Lecture Notes in Mathematics

Sobolev Gradients and Differential Equations

Authors: Neuberger, John

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About this book

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.

Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-540-69594-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Sobolev Gradients and Differential Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1670
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69594-3
DOI
10.1007/BFb0092831
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 152
Topics