Results 1 to 10 of about 371 (68)

Averages and the $\ell^{q,1}$-cohomology of Heisenberg groups [PDF]

arXiv, 2019
Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these ...
Pansu, Pierre, Tripaldi, Francesca
core   +4 more sources

Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group [PDF]

European Journal of Mathematics (2023), 2022
Inthisnote,weprovetheblow-upofsolutionsofthesemilineardamped Klein-Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group.
Ruzhansky, Michael, Sabitbek, Bolys
core   +2 more sources

A certain critical density property for invariant Harnack inequalities in H-type groups [PDF]

arXiv, 2013
We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Guti\'errez and Tournier for the Heisenberg group, we prove a critical
Tralli, Giulio
core   +2 more sources

On an evolution equation in sub-Finsler geometry [PDF]

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj   +2 more sources

Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry

Advanced Nonlinear Studies, 2022
In this article, we establish a Gaffney type inequality, in Wℓ,p{W}^{\ell ,p}-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind noncompact manifolds)
Baldi Annalisa, Tesi Maria Carla, Tripaldi Francesca   +2 more
doaj   +1 more source

Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2022
We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces.
Adamowicz Tomasz, Kijowski Antoni, Soultanis Elefterios   +2 more
doaj   +1 more source

One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain

Nonautonomous Dynamical Systems, 2023
The integro-differential equation of heat conduction with the time-convolution integral on the right side is considered. The direct problem is the initial-boundary problem for this integro-differential equation.
Durdiev Durdimurod Kalandarovich, Jumaev Jonibek Jamolovich   +1 more
doaj   +1 more source

Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group

Advanced Nonlinear Studies, 2022
This article is devoted to the study of the combined effects of logarithmic and critical nonlinearities for the Kirchhoff-Poisson system −M∫Ω∣∇Hu∣2dξΔHu+μϕu=λ∣u∣q−2uln∣u∣2+∣u∣2uinΩ,−ΔHϕ=u2inΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-M\left(\mathop ...
Pucci Patrizia, Ye Yiwei
doaj   +1 more source

Multiplicity of solutions for a class of critical Schrödinger-Poisson systems on the Heisenberg group

Open Mathematics, 2023
We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: ΔHu−μ1ϕ1u=∣u∣2u+Fu(ξ,u,v),inΩ,−ΔHv+μ2ϕ2v=∣v∣2v+Fv(ξ,u,v),inΩ,−ΔHϕ1=u2,−ΔHϕ2=v2,inΩ,ϕ1=ϕ2=u=v=0,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{H}u-{\mu }_{1}{
Li Shiqi, Song Yueqiang
doaj   +1 more source

Liouville theorems for Kirchhoff-type parabolic equations and system on the Heisenberg group

Open Mathematics, 2023
In this article, the Liouville theorems for the Kirchhoff-type parabolic equations on the Heisenberg group were established. The main technique for proving the result relies on the method of test functions.
Shi Wei
doaj   +1 more source