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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Geometry

• Full title: Partial Differential Equations VIII
• Subtitle: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory
• Author: M. A. Shubin, C. Constanda
• Language: English
• Binding: Paperback
• Number of pages: 261
• EAN: 9783642489464
• ISBN: 364248946X
• ID: 07051407
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 417 g
• Dimensions: 235 × 155 × 16 mm
• Date of publishing: 14. April 2012

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