Results 81 to 90 of about 5,405,878 (192)

Partial interior regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups: the sub-quadratic controllable case

Boundary Value Problems, 2017
We consider nonlinear sub-elliptic systems with Dini continuous coefficients for the case 1 < m < 2 $1 ...
Dongni Liao, Jialin Wang, Qiang Yang, Shimin Wu   +3 more
doaj   +1 more source

c horizontal convexity on Carnot groups

, 2010
Given a real-valued function $c$ defined on the cartesian product of a generic Carnot group $\G$ and the first layer $V_1$ of its Lie algebra, we introduce a notion of $c$ horizontal convex ($c$ H-convex) function on $\G$ as the supremum of a suitable family of affine functions; this family is defined pointwisely, and depends strictly on the horizontal
CALOGERO, ANDREA GIOVANNI, PINI, RITA
openaire   +4 more sources

Critical Singular Problems in Carnot Groups

The Journal of Geometric Analysis
Abstract We consider a power-type mild singular perturbation of a Dirichlet semilinear critical problem settled in an open and bounded set in a Carnot group. Here, the term critical has to be understood in the sense of the Sobolev embedding.
Biagi, Stefano, Galeotti, Mattia, Vecchi, Eugenio   +2 more
openaire   +3 more sources

Differential forms in Carnot groups: a variational approach

Bruno Pini Mathematical Analysis Seminar, 2011
Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex of ``intrinsic'' differential forms. In this paper we want to provide an evidence of the intrinsic character of Rumin's complex, in the spirit of the
Annalisa Baldi
doaj  

Hypergenerated Carnot groups

22 ...
Donne, Enrico Le, Nalon, Luca, Paddeu, Nicola, Verzellesi, Simone   +3 more
openaire   +2 more sources

Schrödinger–Hardy system without the Ambrosetti–Rabinowitz condition on Carnot groups

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study the following Schrödinger–Hardy system \begin{equation*} \begin{cases} -\Delta_{\mathbb{G}}u-\mu\frac{\psi^2}{r(\xi)^2}u=F_u(\xi,u,v)\ &{\rm in}\ \Omega, \\ -\Delta_{\mathbb{G}}v-\nu\frac{\psi^2 }{r(\xi)^2}v=F_v(\xi,u,v)\
Wenjing Chen, Fang Yu
doaj   +1 more source

High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential

Abstract and Applied Analysis, 2014
Let {X1,X2,…,Xm} be the basis of space of horizontal vector fields in a Carnot group G=(Rn ...
Pengcheng Niu, Kelei Zhang
doaj   +1 more source

Multiscale phytoplankton dynamics in a coastal system of the eastern English Channel: the Boulogne-sur-Mer coastal area [PDF]

Ocean Science
To study changes in phytoplankton community composition on different timescales, an automated flow cytometer (CytoSub, CytoBuoy b.v.) was deployed at the MAREL Carnot automated monitoring station in Boulogne-sur-Mer (eastern English Channel, France ...
K. Robache, Z. Hubert, C. Gallot, C. Gallot, A. Epinoux, A. P. Louchart, A. P. Louchart, J.-V. Facq, A. Lefebvre, M. Répécaud, V. Cornille, F. Verhaeghe, Y. Audinet, L. Brutier, F. G. Schmitt, L. F. Artigas   +15 more
doaj   +1 more source

Lipschitz and bilipschitz maps on Carnot groups [PDF]

Pacific Journal of Mathematics, 2013
Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure.
openaire   +2 more sources

Intrinsic Lipschitz Graphs Within Carnot Groups [PDF]

, 2016
A Carnot group is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study the notions of intrinsic graphs and of intrinsic Lipschitz graphs within Carnot groups.
Serapioni, Raul Paolo, FRANCHI, BRUNO
core   +1 more source