Partial regularity of minimizers of quasiconvex variational integrals via interpolation

We prove optimal partial regularity of vector-valued minimizers u of the quasiconvex variational integral ∫ F ( x , u , D u ) d x under polynomial growth of its integrand F . We employ a new direct method based on the interpolation of a Sobolev function w between its gradient Dw and the elliptic operator div A D w with constant coefficient A .