Results 141 to 150 of about 1,673 (173)

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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Elements of Potential Theory on Carnot Groups

Functional Analysis and Its Applications, 2018
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Ruzhansky, MV, Suragan, D
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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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Classification of a Class of Nonrigid Carnot Groups

Journal of Lie Theory, 2015
The authors classify up to isomorphism a class of nonrigid Carnot groups. They also identify all \(C^2\) quasiconformal maps of these nonrigid Carnot groups. The results are interesting.
Hughes, Michael R., Staic, Mihai D., Xie, Xiangdong   +2 more
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Classes of Maximal Surfaces on Carnot Groups

Siberian Mathematical Journal, 2020
This paper contains a discussion of graph surfaces in nilpotent Lie groups with sub-Lorentzian geometric structure. Such graph surfaces are a generalization of Euclidean graphs to the setting of contact mappings between appropriately structured nilpotent Lie groups.
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Jet Spaces as Nonrigid Carnot Groups

Journal of Lie Theory, 2005
On the jet spaces \(J^k(\mathbb R^m,\mathbb R^n)\) product is defined, which turns then to Carnot groups. It is emphasized that this product gives rise to a contact structure which coincides with the classical contact structure in the Lie-Bäcklund setting.
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Polar coordinates in Carnot groups

Mathematische Zeitschrift, 2002
In the present paper, the authors describe a procedure for constructing ``polar coordinates'' in a certain class of Carnot groups. They show that the given construction can be carried out in groups of Heisenberg type and they give explicit formulas for the polar coordinate decomposition in that setting. The construction makes use of nonlinear potential
Balogh, Zoltán M., Tyson, Jeremy T.
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Subharmonic functions on Carnot groups

Mathematische Annalen, 2003
The authors develop a potential theory for \(\Delta_G\)-subharmonic functions in \(\mathbb{R}^N\), where \(\Delta_G\) is the sub-Laplacian in a Carnot group \(G\). The main results are analogues to Riesz representation and Poisson-Jensen formulas, Nevanlinna type theorems, and a characterization of the \(\Delta_G\)-Riesz measures of upper bounded ...
Bonfiglioli, Andrea, Lanconelli, Ermanno
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Convexity in Carnot groups

2005
We give an account of recent results and open questions related to the notion of convexity in Carnot groups.
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Key components for Carnot Battery: Technology review, technical barriers and selection criteria

Renewable and Sustainable Energy Reviews, 2022
Yongliang Li, Yulong Ding, Adriano Sciacovelli   +2 more
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