Results 41 to 50 of about 2,812 (235)
Heat and entropy flows in Carnot groups [PDF]
Revista Matemática Iberoamericana, 2019 We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group \mathbb G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on \mathbb G ...
Ambrosio L., Stefani G.
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Subelliptic and parametric equations on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2015 This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for ...
Molica Bisci G, Ferrara M
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BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces, 2015 Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
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On criticality coupled sub-Laplacian systems with Hardy type potentials on Stratified Lie groups
Communications in Analysis and Mechanics, 2023 In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group $ \begin{equation*} \left\{\begin{aligned} & ...
Jinguo Zhang , Shuhai Zhu
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A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2007 In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group.
Alessandro Ottazzi, Alessandro Ottazzi
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Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0. Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on ...
András Domokos, Juan J. Manfredi
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Review of Carnot Battery Technology Commercial Development
Energies, 2022 Carnot batteries are a quickly developing group of technologies for medium and long duration electricity storage. It covers a large range of concepts which share processes of a conversion of power to heat, thermal energy storage (i.e., storing thermal ...
Vaclav Novotny +3 more
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Sharp Hardy Identities and Inequalities on Carnot Groups
Advanced Nonlinear Studies, 2021 In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups ...
Flynn Joshua, Lam Nguyen, Lu Guozhen
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Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain $ $ of $G$ of the form $$ u_t^ (x,t)=\int_{G}\frac{1}{ ^2}K_ (x,y)(u^ (y,t)-u^ (x,t))\,dy, \qquad x\in $$ with $u^ =g(x,t)$ for $x\notin $. For appropriate rescaled kernel $K_ $ we prove that solutions $u^ $, when $ \rightarrow0$, uniformly approximate the ...
Isolda E. Cardoso, Raúl E. Vidal
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Intrinsic regular surfaces in Carnot groups
Bruno Pini Mathematical Analysis SeminarA Carnot group $G$ is a simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces.
Daniela Di Donato
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