Sobolev gradients and differential equations
Author(s)
Bibliographic Information
Sobolev gradients and differential equations
（Lecture notes in mathematics, 1670）
Springer-Verlag, c1997
Available at / 90 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1670RM971019
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Note
Includes bibliographical references (p. [145]-149) and index
Description and Table of Contents
Description
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.
by "Nielsen BookData"
