# zbMATH — the first resource for mathematics

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
##### Keywords:
singular set; Hausdorff dimension; integral functional
Full Text:
##### References:
 [1] Acerbi, E., Fusco, N.: Regularity for minimizers of nonquadratic functionals: the case 1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.