*Published Paper*

**Inserted:** 31 may 2010

**Last Updated:** 5 may 2011

**Journal:** J. Differential Equations

**Volume:** 250

**Number:** 3

**Year:** 2011

**Abstract:**

We establish $C^{1,\gamma}$-partial regularity of minimizers of non autonomous convex integral functionals of the type:
$
\mathcal{F}(u; \Omega):=\int_{\Omega}f(x, Du)\ dx ,
$
with non standard growth conditions into the gradient variable
$$
\frac{1}{L}

\xi ^{{p}} \leq f(x,\xi) \leq L (1+

\xi ^{{q})
}
$$
for a couple of exponents $p,q$ such that
$$
1< p\leq q< \min\left\{p \frac{n}{n-1}, p+1\right\} ,
$$
and $\alpha$- HÃ¶lder continuous dependence with respect to the $x$ variable.
The significant point here is that the distance between the exponents $p$ and $q$ is independent of $\alpha$. Moreover this bound on the gap between the growth and the coercitivity exponents improves previous results in this setting.

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