Results 21 to 30 of about 2,300 (225)
Convex functions on Carnot groups
Revista Matemática Iberoamericana, 2007 We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
P. JUUTINEN +3 more
openaire +6 more sources
Rigidity of 2-Step Carnot Groups [PDF]
The Journal of Geometric Analysis, 2017 Except for minor polishing this version is enriched with two appendices concerning pseudo H-type algebras with J^2-condition. In Appendix A we relate these algebras to division algebras and their split versions.
Mauricio Godoy Molina +3 more
openaire +3 more sources
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
Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 23 ...
Pinamonti A., Speight G.
openaire +4 more sources
Conformality and Q-harmonicity in Carnot groups
Duke Mathematical Journal, 2006 The main theorem of this paper is that 1-quasiconformal maps are smooth in all Carnot groups. This theorem can be used to prove rigidity theorems for quasiconformal maps between open subsets in certain classes of groups without any a priori smoothness assumption.
Capogna, Luca, Cowling, Michael
openaire +4 more sources
Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0. Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on ...
András Domokos, Juan J. Manfredi
doaj +1 more source
On criticality coupled sub-Laplacian systems with Hardy type potentials on Stratified Lie groups
Communications in Analysis and Mechanics, 2023 In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group $ \begin{equation*} \left\{\begin{aligned} & ...
Jinguo Zhang , Shuhai Zhu
doaj +1 more source
Analysis and Geometry in Metric Spaces, 2014 A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups.
Franchi Bruno +2 more
doaj +1 more source
On the Lie Algebra of polarizable Carnot groups [PDF]
Analysis and Mathematical Physics, 2020 Let \(G\) be a Carnot group equipped with a left-invariant sub-Riemannian metric, induced by an inner product \(\langle \cdot, \cdot \rangle\) on the first layer of its Lie algebra \(\mathfrak{g}\). The metric induces a family of \(p\)-sub-Laplacians \(\Delta_p\) on \(G\), where \(\Delta_2\) is the usual sub-Laplacian. Following [\textit{Z. M.
openaire +2 more sources
Harnessing Colloidal Dispersion for Laccase‐Driven Enzymatic Depolymerization of Polystyrene
Angewandte Chemie, EarlyView.Polystyrene (PS), long considered non‐degradable by biocatalytic pathways, can now be broken down under aqueous conditions using atmospheric air and a laccase–mediator system composed of a commercially available fungal enzyme and 1‐hydroxybenzotriazole as small organic mediator.
Manon Pujol +5 more
wiley +2 more sources