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Partial Differential Equations VIII

Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory

Language EnglishEnglish
Book Paperback
Book Partial Differential Equations VIII M. A. Shubin
Libristo code: 07051407
Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,"" Ym)... Full description
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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.

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About the book

Full name Partial Differential Equations VIII
Language English
Binding Book - Paperback
Date of issue 2012
Number of pages 261
EAN 9783642489464
ISBN 364248946X
Libristo code 07051407
Weight 417
Dimensions 155 x 235 x 16
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