Titel: Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schr Dinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
Verlag: Springer
Erscheinungsjahr: 2012
Sprache: Englisch
ISBN-10: 364248946X
ISBN-13: 9783642489464
Einband: Paperback
Zustand: Brand New

�ber diesen Titel

Inhaltsangabe

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.

Von der hinteren Coverseite

This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.

Anbieterinformationen

Zur Homepage des Verk�ufers

Unternehmensdaten des Verk�ufers

Edward Bowditch Ltd
Exstowe, Exton, Exeter, EX3 0PP, United Kingdom

Gesch�ftsbedingungen und Versandinformationen

Verkaufsbedingungen

Legal entity name: Edward Bowditch Ltd
Legal entity form: Limited company
Business correspondence address: Exstowe, Exton, Exeter, EX3 0PP
Company registration number: 04916632
VAT registration: GB834241546
Authorised representative: Mr. E. Bowditch