Analyticity up to the boundary for the divergence equation

Abstract

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