Hypoelliptic Operators

  • Dorina Mitrea
Part of the Universitext book series (UTX)


The concept of hypoelliptic operator is introduced and studied. A classical result, due to L. Schwartz, is proved here to the effect that a necessary and sufficient condition for a linear, constant coefficient differential operator to be hypoelliptic in the entire ambient space is that the named operator possesses a fundamental solution with singular support consisting of the origin alone. In this chapter an integral representation formula and interior estimates for a subclass of hypoelliptic operators are proved as well.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

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