From Ordinary to Partial Differential Equations by Giampiero Esposito

Author:Giampiero Esposito
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(ii)The set

(14.4.3)

has a non-empty interior.

(iii)No limit of as the norm of x approaches 0 is vanishing.

(iv)No limit of the cones as the norm of x approaches infinity has singular generator.

Under such circumstances, the operator a(x, p) is said to be regularly hyperbolic on X.

When X is instead a l-dimensional -smooth manifold, not necessarily complete, the operator a(x, p) is said to be hyperbolic on X when the following conditions hold:(1) a(x, p) is hyperbolic at any point x of X, in the sense specified above.

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