*Published Paper*

**Inserted:** 18 dec 2001

**Journal:** Rend. Ist. Mat. Trieste

**Volume:** XXXI

**Pages:** 203-234

**Year:** 1999

**Abstract:**

\documentclass{article}

\begin{document}

We shall prove everywhere regularity for weak solutions of elliptic systems of the form
$$\sum\frac{\partial}{\partial x_{{i}}a}(x,

Du

)u^{{\alpha}}_{{x}_{{i}}=0$$
}
under general $p$, $q$ growth conditions and in particular for minimizers for a class of variational integrals whose models is $$I(u)=\int_{{\Omega}a}(x)\left( 1+

Du^{{2}\right)}^{{\frac{\alpha}(x)}{2}}dx
$$
\end{document}

**Keywords:**
regularity, Non standard growth conditions