Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

Abstract

We prove the partial Hölder continuity on boundary points for minimizers of quasiconvex non-degenerate functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_Ω f(x,{\bf u},D{\bf u})\,\mathrm{d}x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$-variable, is continuous with respect to $\mathbf{u}$ and has a general growth with respect to the gradient variable.

arXiv commentTo be published in Comm. Pure Appl. Anal