Partial Differential Equations VIII

Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory
Softcover Nachdruck of the original 1. Auflage 1996
ISBN: 978-3-642-48946-4
Verlag: Springer

Buch, Englisch, Band 65, 261 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Shubin, M. A.

Weitere Mitwirkende

Constanda, C.

Dudnikov, P.I.

Fedosov, B.V.

Pavlov, B.S.

Samborski, S.N.

Inhaltsverzeichnis

I. Linear Overdetermined Systems of Partial Differential Equations. Initial and Initial-Boundary Value Problems.- II. Spectral Analysis of a Dissipative Singular Schrödinger Operator in Terms of a Functional Model.- III. Index Theorems.- Author Index.