Analyticity up to the boundary for the divergence equation

We address analytic regularity for the divergence equation $\text{div}u=f$ in $\mathrm{\Omega }$, with $u=0$ on $\mathrm{\partial }\mathrm{\Omega }$, where $\mathrm{\Omega }$ is an arbitrary bounded analytic domain and ${\int }_{\mathrm{\Omega }}fdx=0$. If $f$ is analytic on the closure of $\mathrm{\Omega }$, then we prove that there exists a solution that is analytic on the closure of $\mathrm{\Omega }$.