| 书目名称 | Sobolev Gradients and Differential Equations |
| 编辑 | John William Neuberger |
| 视频video | |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 19971st edition |
| 关键词 | Newton‘s method; Sobolev space; differential equation; numerical analysis; orthogonal projections; partia |
| 版次 | 1 |
| doi | https://doi.org/10.1007/BFb0092831 |
| isbn_ebook | 978-3-540-69594-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer-Verlag Berlin Heidelberg 1997 |
发表于 2025-3-21 18:42:47
