Partial regularity for $ω$-minimizers of quasiconvex functionals

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

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