Hardy-Rellich and second order Poincare identities on the hyperbolic space via Bessel pairs

被引：7

作者：

Berchio, Elvise ^{[1
]}

Ganguly, Debdip ^{[2
]}

Roychowdhury, Prasun ^{[3
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matemat, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Hauz Khas, Dept Math, Indian Inst Technol Delhi, IIT Campus, Delhi 110016, India

[3] Indian Inst Sci Educ & Res, Dept Math, Dr Homi Bhabha Rd, Pune 411008, Maharashtra, India

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 61卷 / 04期

关键词：

26D10; 46E35; 31C12; 35A23; RIEMANNIAN-MANIFOLDS; INEQUALITIES;

D O I：

10.1007/s00526-022-02232-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a family of Hardy-Rellich and Poincare identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Poincare inequalities. All remainder terms provided improve those already known in literature, and all identities hold with same constants for radial operators also. Furthermore, as applications of the main results, second order versions of the uncertainty principle on the hyperbolic space are derived.

引用

页数：24

共 50 条

[41] Existence of multiplicity harmonic and subharmonic solutions for second-order quasilinear equation via Poincare-Birkhoff twist theorem
Cheng, Zhibo
Ren, Jingli
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) : 6801 - 6822
[42] DIFFERENCE SCHEME OF SOLVING CAUCHY-PROBLEM FOR A DEGENERATE HYPERBOLIC SECOND-ORDER EQUATION IN ONE SPACE VARIABLE
KOKOSHKEVICH, A
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1975, 23 (01): : 81 - 85
[43] An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients
Mohanty, RK
APPLIED MATHEMATICS AND COMPUTATION, 2005, 165 (01) : 229 - 236
[44] Finite difference methods for second order in space, first order in time hyperbolic systems and the linear shifted wave equation as a model problem in numerical relativity
Chirvasa, M.
Husa, S.
JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (07) : 2675 - 2696
[45] Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms
Mohanty, R. K.
APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (02) : 1683 - 1690
[46] Second-order structural identification procedure via state-space-based system identification
Alvin, K.F.
Park, K.C.
1600, (32):
[47] SELF-ADJOINT BOUNDARY-VALUE PROBLEMS FOR STRONGLY ELLIPTIC AND HYPERBOLIC SECOND-ORDER EQUATIONS IN HILBERT-SPACE
VAINERMA.LI
DOKLADY AKADEMII NAUK SSSR, 1974, 218 (04): : 745 - 748
[48] Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space
Guermond, Jean-Luc
Nazarov, Murtazo
Popov, Bojan
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2024, 418
[49] RECOVERING DAMPING AND POTENTIAL COEFFICIENTS FOR AN INVERSE NON-HOMOGENEOUS SECOND-ORDER HYPERBOLIC PROBLEM VIA A LOCALIZED NEUMANN BOUNDARY TRACE
Liu, Shitao
Triggiani, Roberto
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (11-12) : 5217 - 5252
[50] A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations
Mohanty, Ranjan K.
Gopal, Venu
ADVANCES IN DIFFERENCE EQUATIONS, 2013, : 1 - 20

← 1 2 3 4 5 →