Metric properties of minimal solutions of discrete periodical variational problems
- 1 February 1989
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 2 (1) , 1-22
- https://doi.org/10.1088/0951-7715/2/1/001
Abstract
The author investigates properties of minimal solutions of multidimensional discrete periodical variational problems. A one-dimensional example of such a problem is the Frenkel-Kontorova model. The author picks out a family of self-conformed solutions, properties of which are exactly the same as in the one-dimensional case. He investigates also non-self-conformed solutions. For translationally invariant Lagrangians he proves that only self-conformed solutions are physically practicable.Keywords
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