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    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory

Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory

Shubin, M. a.
Constanda, C.
Dudnikov, P. I.

Paperback

Series: Encyclopaedia of Mathematical Sciences, Book 65

General MathematicsGeometryPhysics

ISBN10: 364248946X
ISBN13: 9783642489464
Publisher: Springer Nature
Published: Apr 14 2012
Pages: 261
Weight: 0.85
Height: 0.57 Width: 6.14 Depth: 9.21
Language: English
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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