| 书目名称 | Parametrized Measures and Variational Principles |
| 编辑 | Pablo Pedregal |
| 视频video | |
| 丛书名称 | Progress in Nonlinear Differential Equations and Their Applications |
| 图书封面 |  |
| 描述 | Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the cruci |
| 出版日期 | Book 1997 |
| 关键词 | Applied Mathematics; Calculus of variations; Optimization; PDE‘s; calculus; mathematics; mechanics |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-0348-8886-8 |
| isbn_softcover | 978-3-0348-9815-7 |
| isbn_ebook | 978-3-0348-8886-8Series ISSN 1421-1750 Series E-ISSN 2374-0280 |
| issn_series | 1421-1750 |
| copyright | Springer Basel AG 1997 |
发表于 2025-3-21 16:54:44
