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Partial Differential Relations / by Misha Gromov
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 9)
版 | 1st ed. 1986. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1986 |
本文言語 | 英語 |
大きさ | IX, 363 p : online resource |
著者標目 | *Gromov, Misha author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis FREE:Analysis |
一般注記 | 1. A Survey of Basic Problems and Results -- 2. Methods to Prove the h-Principle -- 3. Isometric C?-Immersions -- References -- Author Index 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 requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book HTTP:URL=https://doi.org/10.1007/978-3-662-02267-2 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783662022672 |
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EB00232411 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000110505 |
ISBN | 9783662022672 |
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