Calculus of Variations and Geometric Measure Theory
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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 02 Feb 2022



Inserted: 27 aug 2021
Last Updated: 2 feb 2022

Year: 2021

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


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