Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type Inequalities, and Applications to Riesz Potentials and p-sub-Laplacian Systems
View through CrossRef
AbstractIn this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyapunov-type inequality for the Riesz potential on homogeneous Lie groups. The obtained Lyapunov inequality for the Riesz potential is new already in the classical setting of $\mathbb {R}^{N}$
ℝ
N
. As an application, we give two-sided estimate for the first eigenvalue of the Riesz potential. Also, we obtain Lyapunov inequality for the system of the fractional p-sub-Laplacian equations and give an application to estimate its eigenvalues.
Springer Science and Business Media LLC
Title: Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type Inequalities, and Applications to Riesz Potentials and p-sub-Laplacian Systems
Description:
AbstractIn this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups.
Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyapunov-type inequality for the Riesz potential on homogeneous Lie groups.
The obtained Lyapunov inequality for the Riesz potential is new already in the classical setting of $\mathbb {R}^{N}$
ℝ
N
.
As an application, we give two-sided estimate for the first eigenvalue of the Riesz potential.
Also, we obtain Lyapunov inequality for the system of the fractional p-sub-Laplacian equations and give an application to estimate its eigenvalues.
Related Results
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Background: The dynamics of fractional oscillators are generally described by fractional differential equations, which include the fractional derivative of the Caputo or Riemann-Li...
Hypoelliptic functional inequalities
Hypoelliptic functional inequalities
AbstractIn this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained ine...
Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems
Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems
Abstract
The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculatio...
A conformal geometric point of view on the Caffarelli–Kohn–Nirenberg inequality
A conformal geometric point of view on the Caffarelli–Kohn–Nirenberg inequality
We consider the Caffarelli–Kohn–Nirenberg inequality (CKN in short), introduced by these authors in 1984. We explain why the CKN inequality can be viewed as a Sobolev inequality on...
Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
The paper considers Morrey-type local spaces from LMpθw The main work is the proof of the commutator compactness theorem for the Riesz potential [b,Iα] in local Morrey-type spaces ...
Gagliardo–Nirenberg–Sobolev inequalities in John domains
Gagliardo–Nirenberg–Sobolev inequalities in John domains
We build up a Gagliardo–Nirenberg–Sobolev inequality in John domains and, conversely, under an extra separation property, we show that a bounded domain supporting such a Gagliardo–...
Hardy and Caffarelli-Kohn-Nirenberg inequalities with nonradial weights
Hardy and Caffarelli-Kohn-Nirenberg inequalities with nonradial weights
We study the Hardy type inequalities and Caffarelli-Kohn-Nirenberg type inequalities with nonradial weights of the form \(| x_1| ^{A_1}\cdots| x_N| ^{A_N}/ |x| ^{\lambda}\). For mo...
Liapunov Exponents and Control Theory-Based Stability Analysis and Parameter Optimization Technique for Dynamical Systems with Periodic Variable Coefficients
Liapunov Exponents and Control Theory-Based Stability Analysis and Parameter Optimization Technique for Dynamical Systems with Periodic Variable Coefficients
INTRODUCTION: This is the introductory text Dynamical systems with periodic variable coefficients find extensive use in physics and engineering domains, including nonlinear circuit...