Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals

We consider local minimizers u:R-n superset of -> R-N of variational integrals I[u] := integral(Omega) F(del u) dx, where F is of anisotropic (p, q)-growth with exponents 1 < p <= q < infinity. If F is in a certain sense decomposable, we show that the dimensionless restriction q <= 2p + 2 together with the local boundedness of u implies local integrability of. u for all exponents t <= p + 2. More precisely, the initial exponents for the integrability of the partial derivatives can be increased by two, at least locally. If n = 2, then we use these facts to prove C-1,C-alpha-regularity of u for any exponents 2 <= p <= q.