Displaying similar documents to “Pointwise minimization of supplemented variational problems”

Generalized Jacobi morphisms in variational sequences

Francaviglia, Mauro, Palese, Marcella

Similarity:

Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences. Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with...

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

Second variational derivative of local variational problems and conservation laws

Marcella Palese, Ekkehart Winterroth, E. Garrone (2011)

Archivum Mathematicum

Similarity:

We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we...

Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents

Marcella Palese (2016)

Communications in Mathematics

Similarity:

We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations...

Symmetries in finite order variational sequences

Mauro Francaviglia, Marcella Palese, Raffaele Vitolo (2002)

Czechoslovak Mathematical Journal

Similarity:

We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence....