Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences, 65) - Image 1

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Springer Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences, 65)

Name: Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrodinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences, 65)
Brand: Springer
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Astronomy & Space Science

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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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Brand: Springer
Format: paperback
ASIN: 364248946X
Category: Books > Subjects > Science, Nature & Maths > Astronomy & Space Science
Domain: Amazon UK
Release Date: 14 April 2012
Listed Since: 13 July 2012

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Springer Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences, 65)

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