Displaying similar documents to “Hyperbolic equations and irregularity”

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

Nishitani, Tatsuo (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35L15, Secondary 35L30. In this paper we prove that for non effectively hyperbolic operators with smooth double characteristics with the Hamilton map exhibiting a Jordan block of size 4 on the double characteristic manifold the Cauchy problem is well posed in the Gevrey 6 class if the strict Ivrii-Petkov-Hörmander condition is satisfied.

Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

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Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set Ω ⊂ ℝ n . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization P m , Θ of the principal part P m is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for P m , Θ . Under additional assumptions P m must be locally hyperbolic. ...