*Published Paper*

**Inserted:** 15 oct 2009

**Last Updated:** 2 dec 2013

**Journal:** J. Math. Anal. Appl.

**Volume:** 344

**Number:** 2

**Year:** 2008

**Abstract:**

We prove regularity results for minimizers of functionals
$\cF(u,\Omega) := \int_\Omega f(x,u,Du)\, dx$ in the class $K := \{
u \in W^{1,p(x)}(\Omega,\R): u \ge \psi\}$, where $\psi:\Omega \to
\R$ is a fixed function and $f$ is quasiconvex and fulfills a growth
condition of the type
$$
L^{{}-1}

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

z^{{p}(x)}),
$$
with growth exponent $p:\Omega \to (1,\infty)$.

**Keywords:**
Non standard growth conditions, obstacle problems

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