Hypoelliptic heat kernel inequalities on Lie groups [PDF]
This paper discusses the existence of gradient estimates for the heat kernel of a second order hypoelliptic operator on a manifold. For elliptic operators, it is now standard that such estimates (satisfying certain conditions on coefficients) are ...
Melcher, Tai
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The index of hypoelliptic operators on foliated manifolds
Journal of Noncommutative Geometry, 2010 In [vE1] and [vE2] we presented the solution to the index problem for a class of hypoelliptic operators on closed contact manifolds. The proofs are based on an adaptation of the tangent groupoid method of Alain Connes to hypoelliptic index problems. The methods originally developed for contact manifolds have wider applicability to the index theory of ...
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The Ornstein-Uhlenbeck semigroup in finite dimension. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 Lunardi A, Metafune G, Pallara D.
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The eigenvalues of hypoelliptic operators [PDF]
Journées équations aux dérivées partielles, 1977 A. Menikoff, Johannes Sjöstrand
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A Note on Hypoellipticity of Degenerate Elliptic Operators
Publications of the Research Institute for Mathematical Sciences, 1991 This paper deals with the \(C^ \infty\) hypoellipticity of the following class of linear partial differential operators: \(L = D_ t^{2m} + f(t) D_ x^{2m} + g(t) D_ y^{2m}\), \(m \geq 1\), \(f(t)>0\), \(g(t)>0\) for \(t \neq 0\). Under an assumption on the behaviour of \(\log f(t)\), \(\log g(t)\) for \(t \to 0\) a necessary and a sufficient condition ...
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GENERALIZED WEIGHTED SOBOLEV–MORREY ESTIMATES FOR HYPOELLIPTIC OPERATORS WITH DRIFT ON HOMOGENEOUS GROUPS [PDF]
Let G = ( RN,◦,δλ ) be a homogeneous group, Q be the homogeneous dimension of G, X0,X1,…,Xm be left invariant real vector fields on G and satisfy Hörmander’s rank condition on RN.
Guliyev V.S.
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Joseph Fourier 250th Birthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century. [PDF]
Entropy (Basel), 2019 Barbaresco F, Gazeau JP.
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Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators [PDF]
, 2015 We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift.
Barilari, Davide, Elisa, Paoli
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Local integrability of parametrices of hypoelliptic operators [PDF]
Following Hörmander's work, we investigate in this thesis whether the fundamental solutions of a hypoelliptic operator P(D) in R^n are always locally integrable.
Pezzi, Oscar
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Hardy inequalities on metric measure spaces. [PDF]
Proc Math Phys Eng Sci, 2019 Ruzhansky M, Verma D.
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