Results 11 to 20 of about 195 (41)

On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group [PDF]

, 2015
In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary".
Ruzhansky, Michael, Suragan, Durvudkhan
core   +3 more sources

(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

Open Mathematics, 2020
The paper deals with the existence of solutions for (p,Q)(p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin.
Pucci Patrizia, Temperini Letizia
doaj   +1 more source

The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus

Advanced Nonlinear Studies, 2023
In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Σ\Sigma is discussed.
Case Jeffrey S., Chen Eric, Wang Yi, Yang Paul, Yung Po-Lam   +4 more
doaj   +1 more source

Averages and the $\ell^{q,1}$-cohomology of Heisenberg groups [PDF]

, 2019
Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these ...
Pansu, Pierre, Tripaldi, Francesca
core   +3 more sources

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

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

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, A-P Calderón, B Franchi, B Franchi, B Franchi, B Franchi, B Franchi, B Muckenhoupt, Bruno Franchi, D Applebaum, EB Fabes, F Ferrari, Fausto Ferrari, G Lu, GA Hunt, GB Folland, GB Folland, GN Watson, J Niels, K Bogdan, K Masuda, L Caffarelli, L Capogna, L Hörmander, LA Caffarelli, N Garofalo, P Lévy, PR Stinga, PR Stinga, S-YA Chang, V Magnani, Y Sire   +31 more
core   +1 more source

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
core   +5 more sources

Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups

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, Citti Giovanna, Manfredini Maria   +2 more
doaj   +1 more source

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., Davide Barilari, Juillet N., Luca Rizzi, Montgomery R.   +4 more
core   +2 more sources