Results 221 to 230 of about 12,258,354 (255)

Polar coordinates in Carnot groups

Mathematische Zeitschrift, 2002
We describe a procedure for constructing ”polar coordinates” in a certain class of Carnot groups. We show that our construction can be carried out in groups of Heisenberg type and we give explicit formulas for the polar coordinate decomposition in that setting.
Zoltán M. Balogh, Jeremy T. Tyson
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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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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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Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups

Fractional Calculus and Applied Analysis, 2023
Tong Zhang, Jie-Xiang Zhu
semanticscholar   +1 more source

Hölder Continuity of the Traces of Sobolev Functions to Hypersurfaces in Carnot Groups and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{

Siberian mathematical journal, 2023
S. Basalaev, S. K. Vodopyanov
semanticscholar   +1 more source

$ BV $ -Spaces and the Bounded Composition Operators of $ BV $ -Functions on Carnot Groups

Siberian mathematical journal, 2023
D. A. Sboev
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Classes of Noncontact Mappings of Carnot Groups and Metric Properties

Siberian mathematical journal, 2023
M. Karmanova
semanticscholar   +1 more source

Openness and Discreteness of Mappings of Finite Distortion on Carnot Groups

Siberian mathematical journal, 2023
S. Basalaev, S. K. Vodopyanov
semanticscholar   +1 more source

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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