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Overview"Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,"" Ym) into a vector-valued function I = (h,***, II). We assume at first that all the functions, as well as the coefficients of the differen- tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR , and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A"" such that AA"" = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func- tion Y into the vector-valued function (8y/8x!, 8y/8x2, 8y/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O." Full Product DetailsAuthor: M.A. Shubin , C. Constanda , P.I. Dudnikov , B.V. FedosovPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1996 Volume: 65 Dimensions: Width: 15.50cm , Height: 1.40cm , Length: 23.50cm Weight: 0.417kg ISBN: 9783642489464ISBN 10: 364248946 Pages: 261 Publication Date: 14 April 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI. Linear Overdetermined Systems of Partial Differential Equations. Initial and Initial-Boundary Value Problems.- II. Spectral Analysis of a Dissipative Singular Schrödinger Operator in Terms of a Functional Model.- III. Index Theorems.- Author Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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