*Published Paper*

**Inserted:** 7 mar 2008

**Journal:** Calc. Var. Partial Differential Equations

**Volume:** 27

**Pages:** 179-202

**Year:** 2006

**Abstract:**

We study the limit as $n$ goes to $+\infty$ of the
renormalized solutions $\u_n$ to the nonlinear elliptic problems
\begin{equation**}
-\textrm{div}(a _{n}(x,D u_{n))=\mu,\} \textrm{in\ }\Omega\,, \qquad u_{n=0\,\
}
\textrm{on\ }
\partial\Omega\,,
\end{equation**}
where $\Omega$ is a bounded open set of $R^N$, $N\geq 2$, and
$\mu$ is a Radon measure with bounded variation in $\Omega$. Under
the assumption of G--convergence of the operators
$\mathcal{A}_n(v)=-\textrm{div}(a_n(x,D v))$, defined for
$v\in W^{1,p}_0$, $p>1$,
to the operator $\mathcal{A}_0(v)=-\textrm{div}(a_0(x,D v))$,
we shall prove that the sequence $(u_n)$ admits a subsequence
converging almost everywhere in $\Omega$ to a function $u$ which is a
renormalized solution to the problem
\begin{equation