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The singular set of minima of integral functionals

Abstract:
In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals ∫ ω f(x, v, Dv) dx, where F is suitably convex with respect to Dv and Hölder continuous with respect to (x,v). In particular, we prove that the Hausdorff dimension of the singular set is always strictly less than n, where ω ⊂ ℝ n.
Publication status:
Published

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Publisher copy:
10.1007/s00205-005-0402-5

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume:
180
Issue:
3
Pages:
331-398
Publication date:
2006-06-05
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
URN:
uuid:f824d60c-5a4e-4bca-b596-7128f557ff34
Source identifiers:
19948
Local pid:
pubs:19948
Language:
English

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