FRACTIONAL ORDER KINETIC EQUATIONS AND HYPOELLIPTICITY [PDF]
Analysis and Applications, 2012 We give simple proofs of hypoelliptic estimates for some models of kinetic equations with a fractional order diffusion part. The proofs are based on energy estimates together with the previous ideas of Bouchut and Perthame.
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Global Hypoellipticity for Strongly Invariant Operators
, 2020 In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator $P$ with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that $P$ is globally hypoelliptic.
de Moraes, Wagner Augusto Almeida +1 more
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Hypoelliptic convolution equations in the space 𝒦’ₑ [PDF]
Transactions of the American Mathematical Society, 1986 We consider convolution equations in the space K e ′ \mathcal {K}_e’ of distributions which "grow" no faster than exp ( e k | x |
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Global $L^{p}$ estimates for degenerate Ornstein-Uhlenbeck operators with variable coefficients [PDF]
, 2012 We consider a class of degenerate Ornstein-Uhlenbeck operators in $\mathbb{R}^{N}$, of the kind [\mathcal{A}\equiv\sum_{i,j=1}^{p_{0}}a_{ij}(x) \partial_{x_{i}x_{j}}^{2}+\sum_{i,j=1}^{N}b_{ij}x_{i}\partial_{x_{j}}%] where $(a_{ij})$ is symmetric ...
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Theory of B(X)‐Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators.
Yoritaka Iwata, Ricardo Weder
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The sharp maximal function approach to $L^{p}$ estimates for operators structured on H\"{o}rmander's vector fields [PDF]
, 2015 We consider a nonvariational degenerate elliptic operator structured on a system of left invariant, 1-homogeneous, H\"ormander's vector fields on a Carnot group in $R^{n}$, where the matrix of coefficients is symmetric, uniformly positive on a bounded ...
Bramanti, Marco, Toschi, Marisa
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Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory [PDF]
, 2007 In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\LL(\Gc(\R^n),\wt{\C})$. After having proved the existence of a fundamental solution for a large class of partial differential operators ...
Garetto, Claudia
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Hypoelliptic regularity in kinetic equations
Journal de Mathématiques Pures et Appliquées, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Null-controllability of hypoelliptic quadratic differential equations [PDF]
Journal de l’École polytechnique — Mathématiques, 2017 We study the null-controllability of parabolic equations associated with a general class of hypoelliptic quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols.
Beauchard, Karine, Pravda-Starov, Karel
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Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields
, 2018 Let $L_j = \partial_{t_j} + (a_j+ib_j)(t_j) \partial_x, \, j = 1, \dots, n,$ be a system of vector fields defined on the torus $\mathbb{T}_t^{n}\times\mathbb{T}_x^1$, where the coefficients $a_j$ and $b_j$ are real-valued functions belonging to the ...
de Medeira, Cleber +2 more
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