Results 121 to 130 of about 214,338 (244)

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

A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries [PDF]

arXiv, 2016
Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.
arxiv  

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  

Existence of infinitely many solutions for critical sub-elliptic systems via genus theory

Communications in Analysis and Mechanics
We are devoted to the study of the following sub-Laplacian system with Hardy-type potentials and critical nonlinearities $ \begin{equation*} \left\{\begin{aligned} -\Delta_{\mathbb{G}}u-\mu_{1}\frac{\psi^{2}u}{\text{d}(z)^{2}} = \lambda_{1}\frac{\psi^{
Hongying Jiao, Shuhai Zhu , Jinguo Zhang
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Representation formulas and Fatou-Kato theorems for heat operators on stratified groups [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2005
In this note, we provide a characterization of non-negative L-caloric functions on strips, where L is a sub-Laplacian on a stratified group. We prove representation results, Fatou-type and uniqueness theorems analogous to the classical Poisson Stieltjes ...
Andrea Bonfiglioli, Francesco Uguzzoni
doaj  

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

Existence of optimizers of the Stein-Weiss inequalities on Carnot groups [PDF]

arXiv, 2014
This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to Carnot groups plays an important role in our proof. Unlike known treatment to the Hardy-Littlewood-Sobolev inequality on Heisenberg group, our arguments relate to the powers ...
arxiv  

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  

Stratified $β$-numbers and traveling salesman in Carnot groups [PDF]

arXiv, 2019
We introduce a modified version of P. Jones's $\beta$-numbers for Carnot groups which we call {\it stratified $\beta$-numbers}. We show that an analogue of Jones's traveling salesman theorem on 1-rectifiability of sets holds for any Carnot group if we replace previous notions of $\beta$-numbers in Carnot groups with stratified $\beta$-numbers.
arxiv  

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   +3 more sources