Results 11 to 20 of about 223 (28)

The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus

Advanced Nonlinear Studies, 2023
In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Σ\Sigma is discussed.
Case Jeffrey S., Chen Eric, Wang Yi, Yang Paul, Yung Po-Lam   +4 more
doaj   +1 more source

Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case

Advances in Nonlinear Analysis, 2020
We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group.
Wang Jialin, Zhu Maochun, Gao Shujin, Liao Dongni   +3 more
doaj   +1 more source

Partial Hölder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group

Advances in Nonlinear Analysis, 2018
We consider nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group and prove partial Hölder continuity results for weak solutions using a generalization of the technique of 𝒜{\mathcal{A}}-harmonic approximation.
Wang Jialin, Manfredi Juan J.
doaj   +1 more source

Existence for (p, q) critical systems in the Heisenberg group

Advances in Nonlinear Analysis, 2019
This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
doaj   +1 more source

Weighted Caffarelli–Kohn–Nirenberg type inequalities related to Grushin type operators

Advances in Nonlinear Analysis, 2016
We consider the Grushin type operator on ℝxd×ℝyk{\mathbb{R}^{d}_{x}\times\mathbb{R}^{k}_{y}} of the ...
Song Manli, Li Wenjuan
doaj   +1 more source

Existence results for critical growth Kohn-Laplace equations with jumping nonlinearities

Demonstratio Mathematica
This article is concerned with the existence of nontrivial solutions to critical growth Kohn-Laplace equations with jumping nonlinearities. Or, more specifically, we consider the following Kohn-Laplace problem: −ΔHu=bu+−au−+∣u∣Q∗−2u,inΩ,u=0,on∂Ω,\left ...
An Yu-Cheng, Tian Guai-Qi, An Bi-Jun
doaj   +1 more source

Hardy Type Inequalities for $\Delta_\lambda$-Laplacians

, 2015
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved.
Kogoj, A. E., Sonner, S.
core   +3 more sources

On an evolution equation in sub-Finsler geometry

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   +1 more source

Decay estimates for fractional wave equations on H-type groups

, 2016
The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{it\Delta^\alpha ...
Song, Manli
core   +2 more sources

Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups

, 2015
We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space.
Bonfiglioli, Andrea, Kogoj, Alessia E.
core   +1 more source