Results 231 to 240 of about 12,282,130 (266)

Subharmonic functions on Carnot groups

Mathematische Annalen, 2003
Many results of classical Potential Theory are extended to sub-Laplacians ▵𝔾 on Carnot groups 𝔾. Some characterizations of ▵𝔾-subharmonicity, representation formulas of Poisson-Jensen's kind and Nevanlinna-type theorems are proved. We also characterize the Riesz-measure related to bounded-above ▵𝔾-subharmonic functions in ℝ N
Ermanno Lanconelli, Andrea Bonfiglioli
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A coupling strategy for Brownian motions at fixed time on Carnot groups using Legendre expansion

Electronic Journal of Probability
We propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups.
M. Arnaudon, Magalie B'en'efice, Michel Bonnefont, Delphine F'eral   +3 more
semanticscholar   +1 more source

WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS

Communications in Contemporary Mathematics, 2012
In this paper we define Maxwell's equations in the setting of the intrinsic complex of differential forms in Carnot groups introduced by M. Rumin. It turns out that these equations are higher-order equations in the horizontal derivatives. In addition, when looking for a vector potential, we have to deal with a new class of higher-order evolution ...
FRANCHI, BRUNO, TESI, MARIA CARLA
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Working fluid design and performance optimization for the heat pump-organic Rankine cycle Carnot battery system based on the group contribution method

Energy Conversion and Management, 2023
Hongna Qiao, Xiaohui Yu, B. Yang
semanticscholar   +1 more source

On Gradient Estimates of the Heat Semigroups on Step-Two Carnot Groups

Potential Analysis
In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry-\'Emery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three ...
Sheng-Chen Mao, Ye Zhang
semanticscholar   +1 more source

Homogenization and Convergence of Correctors in Carnot Groups

Communications in Partial Differential Equations, 2005
ABSTRACT We consider homogenization of differential operators of the form where is a family of linearly independent vector fields in ℝ N that by commutation generate the Lie algebra of a Carnot group, a ij (ξ) are periodic functions in the sense of the group, and δ1/e are the dilations in the group. We establish Meyers type estimates for the horizontal
FRANCHI, BRUNO, Gutiérrez C. E., van Nguyen T.   +2 more
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Quasiregular maps on Carnot groups

Journal of Geometric Analysis, 1997
In this paper we initiate the study of quasiregular maps in a sub-Riemannian geometry of general Carnot groups. We suggest an analytic definition for quasiregularity and then show that nonconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type; we further establish, under the same ...
Juha Heinonen, Juha Heinonen, Ilkka Holopainen, Ilkka Holopainen   +3 more
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Liouville-Type Theorems for CC-F-Harmonic Maps into a Carnot Group

Journal of Geometric Analysis, 2020
Guoqing He, Jing Li, P. Zhao
semanticscholar   +1 more source

Composition operators in weighted Sobolev spaces on the Carnot group

Siberian mathematical journal, 2015
N. Evseev
semanticscholar   +2 more sources

Mikhlin’s problem on Carnot groups

Siberian Mathematical Journal, 2008
We consider one class of singular integral operators over the functions on domains of Carnot groups. We prove the L p boundedness, 1 ∞, for the operators of this class. Similar operators over the functions on domains of Euclidean space were considered by Mikhlin.
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