Springer
Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schr?dinger Operator Index Theory
Product Code:
9783642489464
ISBN13:
9783642489464
Condition:
New
$108.02
Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schr?dinger Operator Index Theory
$108.02
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.
| Author: M. a. Shubin |
| Publisher: Springer |
| Publication Date: Apr 14, 2012 |
| Number of Pages: 261 pages |
| Binding: Paperback or Softback |
| ISBN-10: 364248946X |
| ISBN-13: 9783642489464 |
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