Helmholtz's inverse problem of the discrete calculus of variations

被引：6

作者：

Bourdin, Loic ^{[1
]}

Cresson, Jacky ^{[1
]}

机构：

[1] Univ Pau & Pays Adour, F-64000 Pau, France

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2013年 / 19卷 / 09期

关键词：

difference equations; Lagrangian systems; Helmholtz's problem; discrete calculus of variations;

D O I：

10.1080/10236198.2012.754435

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive the discrete version of the classical Helmholtz's condition. Precisely, we state a theorem characterizing second-order finite difference equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.

引用

页码：1417 / 1436

页数：20

共 50 条

[21] Inverse source problem for discrete Helmholtz equation
Novikov, Roman
Sharma, Basant Lal
[J]. INVERSE PROBLEMS, 2024, 40 (10)
[22] New progress in the inverse problem in the calculus of variations
Thoan Do
Prince, Geoff
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 45 : 148 - 179
[23] Presymplectic current and the inverse problem of the calculus of variations
Khavkine, Igor
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (11)
[24] The inverse problem of the calculus of variations in higher space
Davis, David R.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1928, 30 (1-4) : 710 - 736
[25] An inverse problem of the calculus of variations for multiple integrals
La Paz, Lincoln
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1930, 32 (1-4) : 509 - 519
[26] The inverse problem of the calculus of variations: Separable systems
Crampin, M
Prince, GE
Sarlet, W
Thompson, G
[J]. ACTA APPLICANDAE MATHEMATICAE, 1999, 57 (03) : 239 - 254
[27] An EDS approach to the inverse problem in the calculus of variations
Aldridge, J. E.
Prince, G. E.
Sarlet, W.
Thompson, G.
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (10)
[28] THIRTY YEARS OF THE INVERSE PROBLEM IN THE CALCULUS OF VARIATIONS
Saunders, D. J.
[J]. REPORTS ON MATHEMATICAL PHYSICS, 2010, 66 (01) : 43 - 53
[29] On the inverse problem in the calculus of variations for piezoelectric media
Northern Jiaotong Univ, Beijing, China
[J]. Fuhe Cailiao Xuebao, 3 (119-123):
[30] Inverse problem of the calculus of variations on Lie groups
Muzsnay, Z
Thompson, G
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2005, 23 (03) : 257 - 281

← 1 2 3 4 5 →