Results 21 to 30 of about 202 (42)

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

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

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

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 review of Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry by Baldi Annalisa; Tesi Maria Carla; Tripaldi Francesca [PDF]

, 2022
articl
NISHIMURA Hirokazu
core  

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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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  

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

Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups

, 2015
We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space.
Bonfiglioli, Andrea, Kogoj, Alessia E.
core   +1 more source

Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +1 more source