Results 91 to 100 of about 964 (155)

Multiple solutions for possibly degenerate equations in divergence form

Electronic Journal of Differential Equations, 2016
Via variational methods, we establish the existence of at least two distinct weak solutions for the Dirichlet problem associated to a possibly degenerate equation in divergence form.
Andrea Pinamonti
doaj  

Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations [PDF]

We show that the square of Carnot–Carathéodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We first give a proof in the case of ideal Carnot groups,
Zhang, Ye, Liu, Qing, Dragoni, Federica
core   +3 more sources

Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups

Bruno Pini Mathematical Analysis Seminar, 2010
Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S.
Francesco Paolo Montefalcone
doaj  

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source

Global contact and quasiconformal mappings of carnot groups

, 2015
We show that globally defined quasiconformal mappings of rigid Carnot groups are affine, but that globally defined contact mappings of rigid Carnot groups need not be quasiconformal, and a fortiori not ...
Cowling, MG ; https://orcid.org/, Ottazzi, A ; https://orcid.org/   +1 more
core   +1 more source

Semiconcavity, viscosity solutions and the square distance in Carnot groups. [PDF]

We give an overview on semiconcavity, starting from the standard notion, up to more recent generalizations in a different geometrical context, such as Carnot groups; focusing in particular on the viscosity characterization by bounds for second ...
Dragoni, Federica
core   +2 more sources

Hypergenerated Carnot groups

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

cohomology of Carnot groups

, 2018
International audienceWe study the simplicial ℓ q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of ...
Pierre Pansu, Michel Rumin, Pansu, Pierre, Rumin, Michel   +3 more
core   +1 more source

Subriemannian geodesics of Carnot groups of step 3 [PDF]

, 2012
In Carnot groups of step  ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves.
Xiaoping Yang, Yang, Xiaoping, Kanghai Tan, Tan, Kanghai   +3 more
core   +1 more source

Exceptional sets for self-similar fractals in Carnot groups.

, 2010
We consider self-similar iterated function systems in the sub-Rieman- nian setting of Carnot groups. We estimate the Hausdorff dimension of the exceptional set of translation parameters for which the Hausdorff dimension in terms ofthe Carnot-Carath ...
BALOGH Z., MONTI, ROBERTO, BERGER R., TYSON J.   +3 more
core   +1 more source