Partial Differential Equations VIII by Ma Shubin

Partial Differential Equations VIII by Ma Shubin

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.

SKU	Unavailable
ISBN 13	9783642489464
ISBN 10	364248946X
Title	Partial Differential Equations VIII
Author	Ma Shubin
Series	Encyclopaedia Of Mathematical Sciences
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2012-04-14
Number of pages	261
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.