Sobolev Gradients and Differential Equations (1997) (Lecture Notes in Mathematics #1670)
By:
Sign Up Now!
Already a Member? Log In
You must be logged into UK education collection to access this title.
Learn about membership options,
or view our freely available titles.
- 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.
- Copyright:
- 1997
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783540695943
- Related ISBNs:
- 9783540635376
- Publisher:
- Springer Berlin Heidelberg
- Date of Addition:
- 07/15/22
- Copyrighted By:
- N/A
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.