A limiting case in partial regularity for quasiconvex functionals

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