| 书目名称 | Partial Differential Relations | | 编辑 | Mikhael Gromov | | 视频video | | | 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics | | 图书封面 |  | | 描述 | The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requ | | 出版日期 | Book 1986 | | 关键词 | DEX; addition; construction; differential equation; differential geometry; equation; function space; geomet | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-02267-2 | | isbn_softcover | 978-3-642-05720-5 | | isbn_ebook | 978-3-662-02267-2Series ISSN 0071-1136 Series E-ISSN 2197-5655 | | issn_series | 0071-1136 | | copyright | Springer-Verlag Berlin Heidelberg 1986 |
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发表于 2025-3-21 16:14:10
