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Cauchy Problem in the Gevrey Classes

  • Tatsuo Nishitani
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2202)

Abstract

In Chap.  6 we showed that there exists a second order differential operator of spectral type 2 on Σ with bicharacteristics tangent to the double characteristic manifold for which the Cauchy problem is ill-posed in the Gevrey class of order s for any s > 5 even though the Levi condition is satisfied. The best we can expect is the well-posedness in the Gevrey class of order 5 under the Levi condition. This is indeed the case. We prove that for general second order differential operator of spectral type 2 on Σ which may have tangent bicharacteristics, the Cauchy problem is well-posed in the Gevrey class of order 5 under the Levi condition.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tatsuo Nishitani
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonakaJapan

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