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ω-hypoelliptic differential operators of constant strength [PDF]

Journal of Mathematical Analysis and Applications, 2004
We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in Eω(Ω) which is homogeneous ω-hypoelliptic is also σ-hypoelliptic for any weight function σ=O(ω).
Antonio Galbis, David Jornet
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Hypoellipticity and Parabolic Hypoellipticity of Nonlocal Operators under Hörmander’s Condition

Potential Analysis, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiagang Ren, Hua Zhang
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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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Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2017
We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift.
Davide Barilari
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The Hypoelliptic Dirac Operator

2008
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ON A CLASS OF GLOBALLY HYPOELLIPTIC OPERATORS

Mathematics of the USSR-Sbornik, 1973
We consider an operator which is defined on an -dimensional manifold and which is elliptic everywhere outside an -dimensional submanifold . If represents the local coordinates in and is the distance to , then in the coordinates the operator is of the form where is an integer.
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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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ON THE HYPOELLIPTICITY OF INFINITE-DIMENSIONAL DIFFERENTIAL OPERATORS

Mathematics of the USSR-Sbornik, 1977
An infinite-dimensional differential operator with constant coefficients is considered in the paper. A number of necessary conditions for the hypoellipticity of such an operator are proved. These conditions are also sufficient for the hypoellipticity of finite-dimensional differential operators.Bibliography: 10 titles.
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STRICTLY HYPOELLIPTIC OPERATORS WITH CONSTANT COEFFICIENTS

Russian Academy of Sciences. Sbornik Mathematics, 1993
A class of strictly hypoelliptic polynomials is introduced which is intermediate between the wide class of all hypoelliptic polynomials and the class of elliptic polynomials. The necessary conditions for strong hypoellipticity are given and illustrated by some applications to the theory of hypoelliptic operators.
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Hypoelliptic Operators

2023
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