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

[BibTeX]

Submitted Paper

Inserted: 22 jan 2021
Last Updated: 30 jan 2021

Year: 2021

ArXiv: 2101.09472 PDF

Abstract:

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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