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

Partial Hölder continuity for minimizers of discontinuous quasiconvex integrals with VMO coefficients and general growth

created by scilla on 22 Jan 2021
modified on 30 Jan 2021


Submitted Paper

Inserted: 22 jan 2021
Last Updated: 30 jan 2021

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 coefficients


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