We shall prove everywhere regularity for weak solutions of elliptic
systems of the form
\[
\sum\frac{\partial}{\partial x_{i}}a\left(x,\mid Du\mid\right)u_{x_{i}}^{\alpha}=0
\]
under general p, q growth conditions and in particular for minimizers
of a class of variational integrals, both degenerate and non degenerate
ones, whose models are
\[
\begin{array}{c}
I_{1}\left(u\right)\quad=\quad\int_{\Omega}a\left(x\right)\mid Du\mid^{b\left(x\right)}dx,\\
I_{2}\left(u\right)\quad=\quad\int_{\Omega}a\left(x\right)\left(1+\mid Du\mid^{2}\right)^{\frac{b\left(x\right)}{2}}dx.
\end{array}
\]
