Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth (2101.09472v3)

Abstract: We prove the partial H\"older 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.