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Field name	Details
Dewey Class	515
Title	Partial Differential Relations ([EBook]) / by Mikhael Gromov.
Author	Gromov, Mikhael , 1943-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1986.
Physical Details	IX, 363 pages : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 9
ISBN	9783662022672
Summary Note	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.:
Contents note	1. A Survey of Basic Problems and Results -- 2. Methods to Prove the h-Principle -- 3. Isometric C?-Immersions -- References -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02267-2
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Gromov, Mikhael 1943- . Gromov, Mikhael, 1943- . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics . Classification: 515 . 515 (DDC 21) .

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Partial Differential Relations

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