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The singular set of minima of integral functionals. (English) Zbl 1116.49010
The authors provide upper bounds for Hausdorff dimension of the singular set of minima of general variational integrals \[ \int_\Omega F(x, v, Dv)dx, \] 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 \(\Omega \subseteq \mathbb{R} ^n.\)

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
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