Abstract
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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Notes
- 1.
This characterization is not going to play a significant role for us here. For a proof, the interested reader is referred to [35, Theorem 11.1.3, p. 62].
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Mitrea, D. (2018). Hypoelliptic Operators. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-03296-8_6
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DOI: https://doi.org/10.1007/978-3-030-03296-8_6
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Online ISBN: 978-3-030-03296-8
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