Natural boundary conditions in geometric calculus of variations

Rok, strany: 2015, 1531 - 1556

In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework displays complete freedom concerning the topology of $Y$ — the manifold of dependent and independent variables underlying a given problem — as well as the order of its Lagrangian. Our result follows from the natural behavior, under boundary-friendly transformations, of an operator, similar to the Euler map, constructed in the context of relative horizontal forms on jet bundles (or Grassmann fibrations) over $Y$. Explicit examples of natural boundary conditions are obtained when $Y$ is an $(n+1)$-dimensional domain in $\Rⁿ⁺¹$, and the Lagrangian is first-order (in particular, the hypersurface area).

ISO 690:

Moreno, G., Stypa, M. 2015. Natural boundary conditions in geometric calculus of variations. In Mathematica Slovaca, vol. 65, no.6, pp. 1531-1556. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0105

APA:

Moreno, G., Stypa, M. (2015). Natural boundary conditions in geometric calculus of variations. Mathematica Slovaca, 65(6), 1531-1556. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0105