Results 31 to 40 of about 371 (68)
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 +2 more
core +4 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
Moduli of Sub-Laplacians on the second Heisenberg group [PDF]
arXiv, 2023 We solve the contact equivalence problem for generalised sub-Laplacians on $\He^2$ and show that the family of sub-Laplacians on $\He^2$ modulo contact equivalence, is parameterised by $\R^+$
arxiv
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
Morrey-Campanato Functional Spaces for Carnot Groups [PDF]
arXiv, 2023 We shortly review the historical path of Morrey-Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey-Campanato spaces in the framework of Carnot groups.
arxiv
A note on Biharmonic functions on the Thurston geometries [PDF]
, 2017 We construct new explicit proper biharmonic functions on the $3$-dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $H^2\times\rn$ and $S^2\times\rn$.
arxiv +1 more source
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
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
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 +34 more
core +1 more source
On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn
Analysis and Geometry in Metric SpacesThis article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving ...
Liang Sihua +3 more
doaj +1 more source