Large time behavior for the heat equation on Carnot groups [PDF]
arXiv, 2012 We first generalize a decomposition of functions on Carnot groups as linear combinations of the Dirac delta and some of its derivatives, where the weights are the moments of the function. We then use the decomposition to describe the large time behavior of solutions of the hypoelliptic heat equation on Carnot groups.
Rossi, Francesco
arxiv +3 more sources
Loomis–Whitney inequalities on corank 1 Carnot groups [PDF]
Annales Fennici MathematiciIn this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups \(\mathbb{H}^n\) based on the one on the first Heisenberg group \(\mathbb{H}^1\) and the known nonlinear Loomis–Whitney inequality (which
Ye Zhang
openalex +3 more sources
Schrödinger–Hardy system without the Ambrosetti–Rabinowitz condition on Carnot groups
Electronic Journal of Qualitative Theory of Differential EquationsIn this paper, we study the following Schrödinger–Hardy system \begin{equation*} \begin{cases} -\Delta_{\mathbb{G}}u-\mu\frac{\psi^2}{r(\xi)^2}u=F_u(\xi,u,v)\ &{\rm in}\ \Omega, \\ -\Delta_{\mathbb{G}}v-\nu\frac{\psi^2 }{r(\xi)^2}v=F_v(\xi,u,v)\
Wenjing Chen, Fang Yu
doaj +2 more sources
Conformal and CR mappings on Carnot groups [PDF]
Proceedings of the American Mathematical Society, Series B, 2018 We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms.
Cowling, Michael G. +3 more
core +3 more sources
Lipschitz extensions into Jet space Carnot groups [PDF]
arXiv, 2009 The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carath\'eodory distance. The jet spaces give a model for a certain class of Carnot groups, including in particular all Heisenberg groups.
Wenger, Stefan, Young, Robert
arxiv +3 more sources
Hausdorff measure of the singular set of quasiregular maps on Carnot groups [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 Irina Markina
doaj +2 more sources
Horizontal semiconcavity for the square of Carnot-Carathéodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations [PDF]
arXivWe show that the square of Carnot-Carath\'eodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We first give a proof in the case of ideal Carnot groups, based on the simple group structure as well as estimates for the Euclidean semiconcavity.
Federica Dragoni, Qing Liu, Zhang Ye
arxiv +2 more sources
A C^k Lusin approximation theorem for real-valued functions on Carnot groups [PDF]
Indiana University Mathematics Journal, 2023 Marco Capolli +2 more
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Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications [PDF]
Bollettino dell'Unione Matematica Italiana, 2023 In this paper, we provide a different approach to the Alt–Caffarelli–Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the gradient’s norm.
Fausto Ferrari, N. Forcillo
semanticscholar +1 more source
The Fractional Powers of the Sub-Laplacian in Carnot Groups Through an Analytic Continuation [PDF]
Journal of Geometric Analysis, 2023 In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we ...
Francesca Corni, Fausto Ferrari
semanticscholar +1 more source