Abstract. An investigation into the Cartan form and nondegeneracy conditions for field-theoretic Lagrangians based on the Cartan equivalence method. 1. Introduction. In the geometric theory of the calculus of variations in mechanics, the Cartan form, which first arose as the integrand in Hilbert's invariant integral, plays a ubiquitous role. One outstanding problem in the subject is how to define an appropriate Cartan form for a
|
257
|
Geometric Measure Theory
– Federer
- 1969
|
|
80
|
The Classical Groups
– WEYL
- 1939
|
|
73
|
Calculus of Variations
– Gelfand, Fomin
- 1963
|
|
61
|
Multiple integrals in the calculus of variations
– Morrey
- 1966
|
|
41
|
Convexity conditions and existence theorems in nonlinear elasticity
– Ball
- 1977
|
|
32
|
Introduction to the variational bicomplex
– Anderson
- 1992
|
|
31
|
The Theory of Group Characters
– Littlewood
- 1950
|
|
22
|
The Method of Equivalence and Its Applications
– Gardner
- 1989
|
|
19
|
Exterior Differential Systems and the Calculus of Variations
– Griffiths
- 1983
|
|
18
|
The Hamilton-Jacobi Theory in the Calculus of Variations
– Rund
- 1966
|
|
17
|
Transformation groups applied to mathematical physics. Translated from the Russian
– Ibragimov
- 1985
|
|
13
|
Applications of lie groups to differential equations Graduate Texts in Mathematics vol 107
– Olver
- 1986
|
|
10
|
Null Lagrangians, weak continuity, and variational problems of arbitrary order
– Ball, Currie, et al.
- 1981
|
|
10
|
Natural vector bundles and natural differential operators
– Terng
- 1978
|
|
8
|
Théorie Invariantive du Calcul de Variations
– Donder
- 1935
|
|
7
|
Contributions to the study of the equivalence problem of Elie Cartan and its applications to partial and ordinary differential equations
– Kamran
- 1988
|
|
5
|
Calcul des variations et topologie algebrique, Mem
– Dedecker
- 1957
|
|
5
|
A multisymplectic framework for classical field theory and the calculus of variations I. Covariant Hamiltonian formalism
– Gotay
- 1991
|
|
4
|
Über die Variationsrechnung bei mehrfachen
– Carathéodory
- 1929
|
|
4
|
probl`emes d"equivalence, in: Oeuvres Compl`etes
– Les
- 1952
|
|
4
|
Conservation laws and null divergences
– Olver
- 1983
|
|
4
|
1935], Geodesic fields in the calculus of variation for multiple integrals
– Weyl
- 1935
|
|
3
|
An exterior differential systems approach to the Cartan form
– Gotay
- 1991
|
|
3
|
Canonical theories of Lagrangian dynamical systems
– Kastrup
- 1983
|
|
3
|
The equivalence problem and canonical forms for quadratic Lagrangians
– Olver
- 1988
|
|
3
|
Canonical elastic moduli
– Olver
- 1988
|
|
3
|
Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung
– Terpstra
- 1939
|
|
2
|
Aspects of the inverse problem of the calculus of variations, Archivum Mathematicum (Brno) 24
– Anderson
- 1988
|
|
2
|
Internal, external and generalized symmetries, Adv
– Anderson, Kamran, et al.
|
|
2
|
The hook graphs
– Frame, Robinson, et al.
- 1954
|
|
2
|
Equivalence problems for first order Lagrangians on the line
– Kamran, Olver
- 1989
|
|
2
|
Lepagean forms in higher order variational theory, in
– Krupka
- 1983
|
|
2
|
Canonical anisotropic elastic moduli, in: Modern Theory of Anisotropic Elasticity and Applications
– Olver
- 1991
|
|
1
|
Extension of the classical Cartan form, Phys
– Betounes
- 1984
|
|
1
|
The Cartan equivalence problem for first order Lagrangians in m independent and N dependent variables, M.Sc
– Bodnar
- 1986
|
|
1
|
On notions of equivalence of variational problems with one independent variable, Contemp
– Bryant
- 1987
|
|
1
|
un probl`eme d"equivalence et la th'eorie des espaces m'etriques g'en'eralis'es, in
– Cartan, Sur
- 1955
|
|
1
|
Symmetric and antisymmetric outer plethysms of Schur functions, Atomic Data and Nuclear Data Tables 32
– Egecioglu, Remmel
- 1985
|
|
1
|
Equivalence of one dimensional Lagrangian field theories in the plane I, in: Global Differential Geometry and Global Analysis
– Gardner, Shadwick
- 1985
|
|
1
|
une question de calcul des variations
– Hadamard, Sur
- 1902
|
|
1
|
Equivalence of higher order Lagrangians II. The Cartan form for particle Lagrangians
– Hsu, Kamran, et al.
- 1989
|
|
1
|
Le probl`eme d"equivalence `a une divergence pr`es dans le calcul des variations des int'egrales multiples
– Kamran, Olver
- 1989
|
|
1
|
Equivalence of higher order Lagrangians I. Formulation and reduction
– Kamran, Olver
- 1991
|
|
1
|
Mehrdimensionale Variationsrechnung, Birkhauser
– Klotzler
- 1970
|
|
1
|
On the Hamilton form in second order calculus of variations
– Krupka, Step'ankov'a
- 1983
|
|
1
|
The Hamiltonian formulation of regular r th order Lagrangian field theories
– Shadwick
- 1982
|
|
1
|
The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity
– Sivaloganathan
- 1988
|
|
1
|
Gordan's theorem for double binary forms
– Turnbull
|
|
1
|
A geometrical interpretation of the complete system of the double binary (2,2) form
– Turnbull
|
|
