Calculus of Variations and Geometric Measure Theory

J. Ok - G. Scilla - B. Stroffolini

Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

created by scilla on 27 Aug 2021
modified on 10 Nov 2022


Published Paper

Inserted: 27 aug 2021
Last Updated: 10 nov 2022

Journal: Comm. Pure Appl. Anal.
Volume: 21
Number: 12
Pages: 4173-4214
Year: 2021
Doi: 10.3934/cpaa.2022140

ArXiv: 2108.11796 PDF


We prove the partial Hölder continuity on boundary points for minimizers of quasiconvex non-degenerate 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, is continuous with respect to ${\bf u}$ and has a general growth with respect to the gradient variable.

Keywords: Morrey estimates, general growth, VMO condition, boundary partial regularity