Hypoelliptic second order differential equations

@article{Hrmander1967HypoellipticSO,
  title={Hypoelliptic second order differential equations},
  author={Lars H{\"o}rmander},
  journal={Acta Mathematica},
  year={1967},
  volume={119},
  pages={147-171}
}
  • L. Hörmander
  • Published 1 December 1967
  • Mathematics
  • Acta Mathematica
that is, if u must be a C ~ function in every open set where Pu is a C ~ function. Necessary and sufficient conditions for P to be hypoelliptic have been known for quite some time when the coefficients are constant (see [3, Chap. IV]). I t has also been shown tha t such equations remain hypoelliptic after a perturbation by a "weaker" operator with variable coefficients (see [3, Chap. VIII) . Using pseudo-differential operators one can extend the class of admissible perturbations further; in… 
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