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

ISBN 10: 364248946X / ISBN 13: 9783642489464

Edité par Springer, 2012

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N° de réf. du vendeur ria9783642489464_new

Détails bibliographiques

• Titre: Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
• Éditeur: Springer
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 364248946X
• ISBN à 13 chiffres: 9783642489464
• Reliure: Couverture souple
• État de l'article: New

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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.