The Library
On Artin's braid group and polyconvexity in the calculus of variations
Tools
Taheri, Ali (2003) On Artin's braid group and polyconvexity in the calculus of variations. Journal of the London Mathematical Society, Vol.67 (No.3). pp. 752-768. doi:10.1112/S0024610703004253 ISSN 0024-6107.
|
PDF
WRAP_taheri_artins_braid_group.pdf - Requires a PDF viewer. Download (214Kb) |
Official URL: http://dx.doi.org/10.1112/S0024610703004253
Abstract
Let Ω ⊂ 2 be a bounded Lipschitz domain and let
F : Ω × 2×2
+
−→
be a Carathèodory integrand such that F (x, ·) is polyconvex for L2-a.e. x ∈ Ω. Moreover assume that
F is bounded from below and satisfies the condition F (x, ξ) ∞ as det ξ 0 for L2-a.e. x ∈ Ω. The paper describes the effect of domain topology on the existence and multiplicity of strong local minimizers of the functional
[u] :=
Ω
F (x,∇u (x)) dx,
where the map u lies in the Sobolev space W1,p
id (Ω,2) with p 2 and satisfies the pointwise condition
det ∇u (x) > 0 for L2-a.e. x ∈ Ω. The question is settled by establishing that [·] admits a set of strong
local minimizers on W1,p id (Ω,2) that can be indexed by the group n ⊕ n, the direct sum of Artin’s pure braid group on n strings and n copies of the infinite cyclic group. The dependence on the domain topology is through the number of holes n in Ω 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 | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Braid theory, Mathematical optimization, Coxeter groups, Calculus of variations, Lipschitz spaces, Sobolev spaces | ||||
Journal or Publication Title: | Journal of the London Mathematical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0024-6107 | ||||
Official Date: | June 2003 | ||||
Dates: |
|
||||
Volume: | Vol.67 | ||||
Number: | No.3 | ||||
Page Range: | pp. 752-768 | ||||
DOI: | 10.1112/S0024610703004253 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year