| 书目名称 | The Monge—Ampère Equation | | 编辑 | Cristian E. Gutiérrez | | 视频video | | | 丛书名称 | Progress in Nonlinear Differential Equations and Their Applications | | 图书封面 |  | | 描述 | In recent years, the study of the Monge-Ampere equation has received consider able attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposi tion of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from har monic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f. | | 出版日期 | Book 20011st edition | | 关键词 | PDEs; application; differential geometry; harmonic analysis; linear optimization; maximum principle; nonli | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-0195-3 | | isbn_softcover | 978-1-4612-6656-3 | | isbn_ebook | 978-1-4612-0195-3Series ISSN 1421-1750 Series E-ISSN 2374-0280 | | issn_series | 1421-1750 | | copyright | Springer Science+Business Media New York 2001 |
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发表于 2025-3-21 18:52:01
