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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Partial Differential Relations (Paperback, Softcover reprint of hardcover 1st ed. 1986)
Loot Price: R3,837
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Partial Differential Relations (Paperback, Softcover reprint of hardcover 1st ed. 1986)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 9
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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.
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