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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Partial Differential Equations VIII - Overdetermined Systems Dissipative Singular Schroedinger Operator Index Theory (Paperback, Softcover reprint of the original 1st ed. 1996)
Loot Price: R2,620
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Partial Differential Equations VIII - Overdetermined Systems Dissipative Singular Schroedinger Operator Index Theory (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Encyclopaedia of Mathematical Sciences, 65
Expected to ship within 10 - 15 working days
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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."
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