Results 21 to 30 of about 213 (45)

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

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

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   +3 more sources

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

Starshapedeness for fully-nonlinear equations in Carnot groups [PDF]

, 2018
In this paper we establish the starshapedness of the level sets of the capacitary potential of a large class of fully-nonlinear equations for condensers in Carnot groups, once a natural notion of starshapedness has been introduced.
Dragoni, Federica, Garofalo, Nicola, Salani, Paolo   +2 more
core   +4 more sources

Existence of standing waves for quasi-linear Schrödinger equations on Tn

Advances in Nonlinear Analysis, 2019
This paper is devoted to the study of the existence of standing waves for a class of quasi-linear Schrödinger equations on Tn with dimension n ≥ 3. By construction of a suitable Nash-Moser-type iteration scheme, we overcome the clusters of “small divisor”
Zhao Xin, Yan Weiping
doaj   +1 more source

A certain critical density property for invariant Harnack inequalities in H-type groups

, 2013
We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Guti\'errez and Tournier for the Heisenberg group, we prove a critical
Tralli, Giulio
core   +1 more source

A new critical curve for a class of quasilinear elliptic systems

, 2012
We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non
Bidaut-Véron, Bonfiglioli, Busca, Capogna, Caristi, Cîrstea, D’Ambrosio, D’Ambrosio, D’Ambrosio, D’Ambrosio, Farina, Farina, Filippucci, Folland, Folland, Lair, Lorenzo D’Ambrosio, Maly, Mitidieri, Mitidieri, Mitidieri, Mitidieri, Mitidieri, Phan, Polacik, Pucci, Serrin, Serrin, Souplet, Stein, Teramoto, Trudinger, Trudinger, Yang, Yarur   +34 more
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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

Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group [PDF]

, 2013
In this paper, we investigate the sharp Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. On one hand, we apply the concentration compactness principle to prove the existence of the maximizers. While the approach here gives a different proof
Han, Xiaolong
core