A limiting case in partial regularity for quasiconvex functionals

Abstract

Local minimizers of nonhomogeneous quasiconvex variational integrals with standard $ p $-growth of the type

\begin{document}$ w\mapsto \int \left[F(Dw)-f\cdot w\right]{\,{{\rm{d}}}x} $\end{document}

feature almost everywhere $ \mbox{BMO} $-regular gradient provided that $ f $ belongs to the borderline Marcinkiewicz space $ L(n, \infty) $.