A limiting case in partial regularity for quasiconvex functionals

Abstract

Local minimizers of nonhomogeneous quasiconvex variational integrals with standard $p$-growth of the type $$w\mapsto \int \left[F(Dw)-f\cdot w\right]dx$$ feature almost everywhere $\mbox{BMO}$-regular gradient provided that $f$ belongs to the borderline Marcinkiewicz space $L(n,\infty )$.