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### On Artin's braid group and polyconvexity in the calculus of variations

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UNSPECIFIED.
(2003)
*On Artin's braid group and polyconvexity in the calculus of variations.*
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 67
(Part 3).
pp. 752-768.
ISSN 0024-6107

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1112/S0024610703004253

## Abstract

Let Omega subset of R-2 be a bounded Lipschitz domain and let F : Omega X R-+(2x2) --> R be a Caratheodory integrand such that F (x, (.)) is polyconvex for L-2-a.e. x is an element of Omega. Moreover assume that F is bounded from below and satisfies the condition F(x,xi) SE arrow infinity as det xi SE arrow 0 for L-2-a.e. x is an element of Omega. The paper describes the effect of domain topology on the existence and multiplicity of strong local minimizers of the functional F[u] := integral(Omega) F(x,delu(x))dx, where the map u lies in the Sobolev space W-id(1,p)(Omega,R-2) with p greater than or equal to 2 and satisfies the pointwise condition det delu(x) > 0 for L-2-a.e. x is an element of Omega. The question is settled by establishing that F[(.)] admits a set of strong local minimizers on W-id(1,p)(Omega,R-2) that can be indexed by the group P-n circle plus Z(n), the direct sum of Artin's pure braid group on it strings and n copies of the infinite cyclic group. The dependence on the domain topology is through the number of holes n in Omega and the different mechanisms that give rise to such local minimizers are fully exploited by this particular representation.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES |

Publisher: | LONDON MATH SOC |

ISSN: | 0024-6107 |

Date: | June 2003 |

Volume: | 67 |

Number: | Part 3 |

Number of Pages: | 17 |

Page Range: | pp. 752-768 |

Identification Number: | 10.1112/S0024610703004253 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/9566 |

Data sourced from Thomson Reuters' Web of Knowledge

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