The singular set of minima of integral functionals

Journal article

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.

Authors: Kristensen, J; Mingione, G

• Publication status: Published
• Journal: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
• Volume: 180
• Issue: 3
• Pages: 331-398
• Publication date: 2006-06-01
• DOI: 10.1007/s00205-005-0402-5
• EISSN: 1432-0673
• ISSN: 0003-9527
• Language: English