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The Metivier inequality and ultradifferentiable hypoellipticity

Mathematische Nachrichten
Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Stefan Furdos
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Hypoelliptic Infinitesimal Generators

SIAM Journal on Mathematical Analysis, 1977
In this paper we study semi-group generation by semi-bounded second order differential operators on a noncompact $C^\infty $ manifold. It is shown that the usual regularity assumptions can be relaxed to include hypoelliptic operators of the Hormander type.
Baider, Alberto, Cherkas, Barry
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ON A CRITERION FOR HYPOELLIPTICITY

Mathematics of the USSR-Sbornik, 1971
In this paper a criterion for hypoellipticity is proved which is formulated in terms of certain estimates in the norms, and which is a generalization of a criterion of Treves. With the use of this criterion it is possible to prove the hypoellipticity of certain operators that do not satisfy Hormander's criterion.
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ON A CLASS OF HYPOELLIPTIC OPERATORS

Mathematics of the USSR-Sbornik, 1970
Let the variables in be broken up into two groups , where and . We consider differential operators with polynomial symbols of the form where . We assume that the symbol is quasihomogeneous: and that is elliptic for . We have found a necessary and sufficient condition for operators of this class to be hypoelliptic: namely, that the equation , , have no ...
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ON A FUNCTIONAL INDEX OF HYPOELLIPTICITY

Mathematics of the USSR-Sbornik, 1987
For a special family of hypoelliptic operators containing the semielliptic operators the functional characteristic of hypoellipticity is introduced, which is equivalent to hypoellipticity index in the elliptic case and sharpens it in the general case.
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The Hypoelliptic Dirac Operator

2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Gevrey Hypoellipticity of p-Powers of Non-Hypoelliptic Operators

2004
We characterize the hypoellipticity inC ∞ and GevreyG λ classes of 2-variable PDO’s containing powers of anisotropic principal terms. We use an approach based on methods from microlocal analysis. Conditions are imposed on the coefficients of lower order terms. Also a semilinear version is proposed consideringC ∞ nonlinear perturbations. See Theorem 1.1
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PROBABILISTIC PROBLEMS IN THE THEORY OF HYPOELLIPTICITY

Mathematics of the USSR-Izvestiya, 1985
See the review in Zbl 0578.60056.
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The hypoelliptic superconnections

2013
The purpose of this chapter is to extend the results of [B08, section 3] to the case where ω M is not supposed to be closed. More precisely, let π :M→M be the total space of TX, and let q :M→S be the obvious projection with fibre X.
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ON A CLASS OF HYPOELLIPTIC POLYNOMIALS

Mathematics of the USSR-Sbornik, 1968
Volevich, L. R., Gindkikin, S. G.
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