Partial regularity for $\omega$-minimizers of quasiconvex functionals

Abstract

We establish partial regularity for the $\omega$-minimizers of quasiconvex functionals of power growth. A first-order partial regularity result of $BV$ $\omega$-minimizers is obtained in the linear growth case under a Dini-type condition on $\omega$. Only assuming the smallness of $\omega$ near the origin, we show partial H\"{o}lder continuity in the subquadratic case by considering a normalised excess.