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

Jihoon Ok, Giovanni Scilla, Bianca Stroffolini

Published 2021-08-26Version 1

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