Displaying similar documents to “The Euler and Helmholtz operators on fibered manifolds with oriented bases”

Uniqueness results for operators in the variational sequence

W. M. Mikulski (2009)

Annales Polonici Mathematici

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We prove that the most interesting operators in the Euler-Lagrange complex from the variational bicomplex in infinite order jet spaces are determined up to multiplicative constant by the naturality requirement, provided the fibres of fibred manifolds have sufficiently large dimension. This result clarifies several important phenomena of the variational calculus on fibred manifolds.

Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

Ken Shirakawa (2009)

Banach Center Publications

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In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of...

On the inverse problem of the calculus of variations for ordinary differential equations

Olga Krupková (1993)

Mathematica Bohemica

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Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given.

The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories

Jana Musilová, Stanislav Hronek (2016)

Communications in Mathematics

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As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples...