  We establish local higher integrability and differentiability results for
minimizers of variational integrals $$ \mathfrak{F}(v,\Omega) = \int_{\Omega}
/! F(Dv(x)) \, dx $$ over $W^{1,p}$--Sobolev mappings $u \colon \Omega \subset
{\mathbb R}^n \to {\mathbb R}^N$ satisfying a Dirichlet boundary condition. The
integrands $F$ are assumed to be autonomous, convex and of $(p,q)$ growth, but
are otherwise not subjected to any further structure conditions, and we
consider exponents in the range $1<p \leq q < p^{\ast}$, where $p^{\ast}$
denotes the Sobolev conjugate exponent of $p$.
