*Published Paper*

**Inserted:** 26 jul 2001

**Last Updated:** 13 nov 2002

**Journal:** ESAIM:COCV

**Volume:** 7

**Pages:** 495-519

**Year:** 2002

**Abstract:**

We study the integral representation properties of limits of sequences of integral functionals like \,$\int f(x,Du)\,dx$\, under
nonstandard growth conditions of $(p,q)$-type: namely, we assume that
$$
\vert z\vert^{{p}(x)}\leq f(x,z)\leq L(1+\vert z\vert^{{p}(x)})\,.
$$
Under weak assumptions on the continuous function $\px$, we prove $\Gamma$-convergence to integral functionals of the same type.
We also analyse the case of integrands $f(x,u,Du)$ depending explicitly on $u$; finally we weaken the assumption allowing $p(x)$ to be discontinuous on nice sets.

**Keywords:**
Gamma-convergence, Integral representation, Nonstandard growth conditions

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