
Partial Differential Relations
Misha Gromov(Author)
Springer (Publisher)
Published on 1. September 1986
Book
Hardback
IX, 363 pages
978-3-540-12177-0 (ISBN)
Description
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.
More details
Series
Edition
1986 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
IX, 363 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 26 mm
Weight
737 gr
ISBN-13
978-3-540-12177-0 (9783540121770)
DOI
10.1007/978-3-662-02267-2
Schweitzer Classification
Other editions
Additional editions

Person
Mikhail Leonidovich Gromov is a French-Russian mathematician. He is a Professor at the Institut des Hautes Études Scientifiques and New York University. During his outstanding career he has received many honors and prizes; most recently he was awarded the Abel Prize "for his revolutionary contributions to geometry." He is a prolific author with more than 150 scientific publications including 8 books.
Content
1. A Survey of Basic Problems and Results.- 2. Methods to Prove the h-Principle.- 3. Isometric C?-Immersions.- References.- Author Index.