| 书目名称 | The Pullback Equation for Differential Forms |
| 编辑 | Gyula Csató,Bernard Dacorogna,Olivier Kneuss |
| 视频video | |
| 概述 | The only book to systematically explore the equivalence of differential forms.Rigorously presents Hodge decomposition and several versions of the Poincaré lemma.Includes a very rare, extended study of |
| 丛书名称 | Progress in Nonlinear Differential Equations and Their Applications |
| 图书封面 |  |
| 描述 | .An important question in geometry and analysis is to know when two .k.-forms .f .and g are equivalent through a change of variables. The problem is therefore to find a map .φ .so that it satisfies the pullback equation: .φ.*.(.g.) = .f... .In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases .k .= 2 and .k .= .n., but much less when 3 ≤ .k .≤ .n.–1. The present monograph provides the first comprehensive study of the equation.. .The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case .k .= .n., and then the case 1≤ .k .≤ .n.–1 with special attention on the case .k .= 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in |
| 出版日期 | Book 2012 |
| 关键词 | Hodge decomposition; Hölder spaces; Poincaré lemma; equivalence of differential forms; global Darboux th |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-8176-8313-9 |
| isbn_ebook | 978-0-8176-8313-9Series ISSN 1421-1750 Series E-ISSN 2374-0280 |
| issn_series | 1421-1750 |
| copyright | Springer Science+Business Media, LLC 2012 |
发表于 2025-3-21 18:35:18
