Summary
In this paper we consider partial differential operators of the type P(x, D)= Pm(D)+Q(x, D), where the constant coefficient principal part Pm is supposed to be hyperbolic-elliptic. We study the propagation of Gevrey singularities for solutions u of the equation P(x, D) u=f, for ultradistributions f, finding exactly to which spaces of ultradistribuiions u microlocally belongs. The results are obtained by constructing a fundamental solution for P when the lower order part Q is with constant coefficients, and a parametrix otherwise.
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Cicognani, M., Corli, A. Propagation of singularities for operators with constant coefficient hyperbolic-elliptic principal part. Annali di Matematica pura ed applicata 147, 303–341 (1987). https://doi.org/10.1007/BF01762422
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DOI: https://doi.org/10.1007/BF01762422