Calculus of Variations and Geometric Measure Theory
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C. S. Goodrich - G. Scilla - B. Stroffolini

Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

created by scilla on 22 Jan 2021
modified on 26 Aug 2021


Accepted Paper

Inserted: 22 jan 2021
Last Updated: 26 aug 2021

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Year: 2021

ArXiv: 2101.09472 PDF


We prove the partial Hölder continuity for minimizers of quasiconvex functionals \[ \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\mathrm{d}x, \] where $f$ satisfies a uniform VMO condition with respect to the $x$-variable and is continuous with respect to ${\bf u}$. The growth condition with respect to the gradient variable is assumed a general one.

Keywords: Partial regularity, Morrey estimates, general growth, VMO condition


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