A note on the Cauchy problem for $-D_0^2+2x_1D_0D_2+D_1^2+x_1^3D_2^2+\sum_{j=0}^2b_jD_j$
Analysis of PDEs
2022-08-17 v1
Abstract
In this note, we improve a previously proven non-solvability result of the Cauchy problem for the Cauchy problem in the Gevrey class for a homogeneous second-order differential operator mentioned in the title. We prove that the Cauchy problem for this operator is not locally solvable at the origin for any lower order term in the Gevrey class of order greater than 5, lowering the previously obtained Gevrey order 6.
Keywords
Cite
@article{arxiv.2208.07534,
title = {A note on the Cauchy problem for $-D_0^2+2x_1D_0D_2+D_1^2+x_1^3D_2^2+\sum_{j=0}^2b_jD_j$},
author = {Tatsuo Nishitani},
journal= {arXiv preprint arXiv:2208.07534},
year = {2022}
}
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12 pages