Results 21 to 30 of about 14,687 (238)
Rigidity of 2-Step Carnot Groups [PDF]
The Journal of Geometric Analysis, 2017 Except for minor polishing this version is enriched with two appendices concerning pseudo H-type algebras with J^2-condition. In Appendix A we relate these algebras to division algebras and their split versions.
Mauricio Godoy Molina +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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Hilbert-Haar coordinates and Miranda's theorem in Lie groups
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero
András Domokos, Juan J. Manfredi
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Harnack inequality for fractional sub-Laplacians in Carnot groups [PDF]
, 2013 In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre ...
A Bonfiglioli +31 more
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Intrinsic Lipschitz Graphs Within Carnot Groups [PDF]
The Journal of Geometric Analysis, 2015 Carnot groups are connected, simply connected, nilpotent Lie groups whose Lie algebra admits a stratification. Hence, the easiest nontrivial class of examples of Carnot groups are Heisenberg groups. In this well-written paper, the authors examine a general notion of intrinsic submanifolds in Carnot groups, called \textit{Intrinsic Lipschitz graphs ...
FRANCHI, BRUNO, Serapioni, Raul Paolo
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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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On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Abstract and Applied Analysis, 2020 We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
Cecilia De Zan, Pierpaolo Soravia
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Convex functions on Carnot groups
Revista Matemática Iberoamericana, 2007 We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
P. JUUTINEN +3 more
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Nonexistence Results for Semilinear Equations in Carnot Groups
Analysis and Geometry in Metric Spaces, 2013 In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot ...
Ferrari Fausto, Pinamonti Andrea
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Measure contraction properties of Carnot groups [PDF]
, 2016 We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$.
Rizzi, Luca
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