Partial regularity for $BV$ $ω$-minimizers of quasiconvex functionals

Zhuolin Li

Published 2022-01-26Version 1

We establish the partial regularity for the $\omega$-minimizers in $BV$ of variational functionals with strongly quasiconvex integrands of linear growth. The partial regularity of the derivative is established when $\omega$ satisfies some Dini-type condition. Removing this assumption and only assuming the smallness of $\omega$ near the origin, we managed to show the partial H\"{o}lder continuity of the $\omega$-minimizers themselves with a normalised excess.