Partial Differential Equations VIII

Name: Partial Differential Equations VIII
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642489464
Price: 89.86 EUR
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Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory

Autor: M. A. Shubin, C. Constanda

Jazyk:

Väzba: Brožovaná

Vydavateľ: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Dostupnosť: Skladom u dodávateľa

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Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,"" Ym)...

Informácie o knihe

Autor

M. A. Shubin, C. Constanda

Jazyk

Angličtina

Väzba

Kniha - Brožovaná

Vydalo

2012

Stránok

261

EAN

9783642489464

ISBN

364248946X

Enbook ID

07051407

Vydavateľ

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Hmotnosť

417

Rozmery

155 x 235 x 16

Kompletný popis

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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Partial Differential Equations VIII

Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory

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