Results 21 to 30 of about 371 (68)
Analysis and Geometry in Metric Spaces, 2013 In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0.
Capogna Luca +2 more
doaj +1 more source
Existence and Uniqueness results for linear second-order equations in the Heisenberg group [PDF]
, 2017 In this manuscript, we prove uniqueness and existence results of viscosity solutions for a class of linear second-order equations in the Heisenberg group.
Ochoa, Pablo Daniel, Ruiz, Julio Alejo
core +1 more source
Attainable set for rank 3 step 2 free Carnot group with positive controls
, 2022 We find the attainable set for a control system on the free Carnot group of rank $3$ and step $2$ with positive controls. This kind of control systems is connected with the theory of free Lie semigroups; with some estimates for probabilities of ...
Podobryaev, A. V.
core +1 more source
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
core +1 more source
A counterexample to the monotone increasing behavior of an Alt-Caffarelli-Friedman formula in the Heisenberg group [PDF]
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023), 2022 In this paper we provide a counterexample about the existence of an increasing monotonicity behavior of a function introduced in \cite{FeFo}, companion of the celebrated Alt-Caffarelli-Friedman monotonicity formula, in the noncommutative framework.
arxiv +1 more source
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
doaj +1 more source
Geometric Hardy Inequalities on Starshaped Sets [PDF]
, 2021 We present geometric Hardy inequalities on starshaped sets in Carnot groups.
Ruzhansky, M, Sabitbek, B, Suragan, D
core +3 more sources
Sharp measure contraction property for generalized H-type Carnot groups [PDF]
, 2017 We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group.
Bonfiglioli A. +4 more
core +2 more sources
Lp - Liouville theorems for invariant evolution equations [PDF]
, 2014 Some Liouville-type theorems in Lebesgue spaces for several classes of evolution equations are presented. The involved operators are left invariant with respect to Lie group composition laws.
Kogoj, Alessia E.
core +3 more sources
Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups
Advances in Nonlinear Analysis, 2018 Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj +1 more source