Weighted anisotropic Hardy and Rellich type inequalities for general vector fields

被引：0
作者：
Michael Ruzhansky
Bolys Sabitbek
Durvudkhan Suragan
机构：
[1] Ghent University,Department of Mathematics: Analysis, Logic and Discrete Mathematics
[2] Queen Mary University of London,School of Mathematical Sciences
[3] Institute of Mathematics and Mathematical Modeling,Department of Mechanics and Mathematics
[4] Al-Farabi Kazakh National University,Department of Mathematics
[5] Nazarbayev University,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2019年 / 26卷
关键词：
Vector fields; Hardy inequality; Rellich inequality; Picone identity; Uncertainty principle; 35A23; 35H20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new as well as many of the fundamental Hardy and Rellich type inequalities which are known in different settings.
引用
收藏
相关论文
共 40 条
[1]  
Barbatis G(2004)A unified approach to improved Trans. Am. Math. Soc. 356 2169-2196
[2]  
Filippas S(1998) Hardy inequalities with best constants Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 217-237
[3]  
Tertikas A(2005)Hardy’s inequalities revisited Ann. Scuola Norm. Sup. Pisa CI. Sci 5 451-486
[4]  
Brezis H(2009)Hardy-type inequalities related to degenerate elliptic differential operators Nonlinear Anal. 70 2855-2869
[5]  
Marcus M(2004)Liouville theorems for anisotropic quasilinear inequalities Differ. Equ. 40 552-564
[6]  
D’Ambrosio L(1998)Some Hardy inequalities on the Heisenberg group Math. Z. 227 511-523
[7]  
D’Ambrosio L(1990)Explicit constants for Rellich inequalities in Ann. Inst. Fourier (Grenoble) 40 313-356
[8]  
D’Ambrosio L(2017)Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation Discrete Contin. Dyn. Syst. 37 2009-2021
[9]  
Davies EB(2018)A unified approach to weighted Hardy type inequalities on Carnot groups Monatsh Math. 186 49-72
[10]  
Hinz AM(2011)A general approach to weighted Rellich type inequalities on Carnot groups Math. Ann. 349 1-57
1234