Results 231 to 240 of about 12,576,498 (281)

Mikhlin’s problem on Carnot groups

Siberian Mathematical Journal, 2008
Summary: We consider one class of singular integral operators over the functions on domains of Carnot groups.
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Quasi-convex Functions in Carnot Groups*

Chinese Annals of Mathematics, Series B, 2007
The authors introduce the concept of \(h\)-quasiconvexity which generalizes the notion of \(h\)-convexity in the Carnot group \(G\). An example of \(h\)-quasiconvex function which is not \(h\)-convex is provided. Some interesting properties similar to those of \(h\)-convex functions on \(G\) are given.
Sun, Mingbao, Yang, Xiaoping
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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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The Agrachev–Barilari–Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $$G_{3,3}$$

Proceedings of the Steklov Institute of Mathematics, 2023
A. Greshnov
semanticscholar   +1 more source

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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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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Optimal estimates of the number of links of basis horizontal broken lines for 2-step Carnot groups with horizontal distribution of corank 1

Russian Universities Reports. Mathematics
For a 2-step Carnot group D_n, "dim" D_n=n+1, with horizontal distribution of corank 1, we proved that the minimal number N_(X_(D_n ) ) such that any two points u,v∈D_n can be joined by some basis horizontal k-broken line (i.e.
A. Greshnov, R. I. Zhukov
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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
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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
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Non co-adapted couplings of Brownian motions on free, step 2 Carnot groups

E S A I M: Probability & Statistics
On the free, step $2$ Carnot groups of rank $n$ $\Ge_n$, the subRiemannian Brownian motion consists in a $\mathbb{R}^n$-Brownian motion together with its $\frac{n(n-1)}{2}$ Lévy areas.
Magalie B'en'efice
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