Generic uniqueness of a minimal solution for variational problems on a torus
We study minimal solutions for one-dimensional variational problems on a torus. We show that, for a generic integrand and any rational number α, there exists a unique (up to translations) periodic minimal solution with rotation number α.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502000842 |
| Summary: | We study minimal solutions for one-dimensional variational
problems on a torus. We show that, for a generic
integrand and any rational number α, there exists a unique
(up to translations) periodic minimal solution with rotation number α. |
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| ISSN: | 1085-3375 1687-0409 |