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Displaying 61 – 80 of 181

Homogeneous Carnot groups related to sets of vector fields

Andrea Bonfiglioli (2004)

Bollettino dell'Unione Matematica Italiana

In this paper, we are concerned with the following problem: given a set of smooth vector fields $X_{1}, \dots, X_{m}$ on $R^{N}$ , we ask whether there exists a homogeneous Carnot group $G = (R^{N}, \circ, δ_{λ})$ such that $\sum_{i} X_{i}^{2}$ is a sub-Laplacian on $G$ . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we exhibit several...

Homogenization of Hamilton-Jacobi equations in Carnot Groups

Bianca Stroffolini (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.

Homogenization of periodic semilinear hypoelliptic PDEs

Alassane Diédhiou, Étienne Pardoux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.

Hörmander systems and harmonic morphisms

Elisabetta Barletta (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a Hörmander system $X = {X_{1}, \dots, X_{m}}$ on a domain $Ω \subseteq 𝐑^{n}$ we show that any subelliptic harmonic morphism $φ$ from $Ω$ into a $ν$ -dimensional riemannian manifold $N$ is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also $φ$ is a submersion provided that $ν \leq m$ and $X$ has rank $m$ . If $Ω = 𝐇_{n}$ (the Heisenberg group) and $X = \{\frac{1}{2} (L_{α} + L_{\bar{α}}), \frac{1}{2 i} (L_{α} - L_{\bar{α}})\}$ , where $L_{\bar{α}} = \partial / \partial {\bar{z}}^{α} - i z^{α} \partial / \partial t$ is the Lewy operator, then a smooth map $φ : Ω \to N$ is a subelliptic harmonic morphism if and only if $φ \circ π : (C (𝐇_{n}), F_{θ_{0}}) \to N$ is a harmonic morphism, where $S^{1} \to C (𝐇_{n}) \overset{π}{\to} \to 𝐇_{n}$ is the canonical circle bundle and $F_{θ_{0}}$ is the Fefferman...

Hypoelliptic and Gevrey hypoelliptic invariant differential operators on certain symmetric spaces

Paul Godin (1982)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hypoelliptic estimates for some linear diffusive kinetic equations

Frédéric Hérau (2010)

Journées Équations aux dérivées partielles

This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations,...

Currently displaying 61 – 80 of 181

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Displaying 61 – 80 of 181

Homogeneous Carnot groups related to sets of vector fields

Homogenization of Hamilton-Jacobi equations in Carnot Groups

Homogenization of periodic semilinear hypoelliptic PDEs

Hörmander systems and harmonic morphisms

Hypoelliptic and Gevrey hypoelliptic invariant differential operators on certain symmetric spaces

Hypoelliptic estimates for some linear diffusive kinetic equations

Hypoelliptic operators with characteristic variety of codimension two and the wave equation

Hypoelliptic operators with double characteristics

Hypoelliptic systems of complex vector fields

Hypoellipticité analytique d'opérateurs transversalement elliptiques

Hypoellipticité analytique pour des opérateurs à caractéristiques multiples - Démonstration élémentaire

Hypoellipticité analytique sur des groupes nilpotents de rang 2 (d'après G. Metivier)

Hypoellipticité d'équations aux dérivées partielles non linéaires

Hypoellipticité d'opérateurs à caractéristiques multiples

Hypoellipticité et paramétrix pour des opérateurs pseudodifférentiels à caractéristiques doubles

Hypoellipticité et régularité locale des solutions faibles des équations aux dérivées partielles du second ordre

Hypoellipticité maximale pour le système de Cauchy-Riemann induit

Hypoellipticité maximale pour le système de Cauchy-Riemann induit

Hypoellipticité pour des groupes nilpotents de rang de nilpotence $3$

Hypoellipticité pour des opérateurs différentiels sur des groupes de Lie nilpotents

Currently displaying 61 – 80 of 181