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Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 5 / October 2022
- Published online by Cambridge University Press:
- 01 December 2021, pp. 1191-1232
- Print publication:
- October 2022
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- Article
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We prove the partial Hölder continuity for minimizers of quasiconvex functionals
where
\begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*}
$f$ 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.
