Calculus of Variations and Geometric Measure Theory

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 27 Sep 2022


Published Paper

Inserted: 22 jan 2021
Last Updated: 27 sep 2022

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 152
Number: 5
Pages: 1191-1232
Year: 2021
Doi: 10.1017/prm.2021.53

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