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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Nishitani, T. (2017). Cauchy Problem in the Gevrey Classes. In: Cauchy Problem for Differential Operators with Double Characteristics. Lecture Notes in Mathematics, vol 2202. Springer, Cham. https://doi.org/10.1007/978-3-319-67612-8_7
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DOI: https://doi.org/10.1007/978-3-319-67612-8_7
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Online ISBN: 978-3-319-67612-8
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