Let \(L\) be an elliptic operator on a domain \(\Omega \subset \mathbb{R}^n\) with analytic coefficients \(a_{\alpha}\). If \(u\in \mathcal{D}'(\Omega)\) satisfies

\begin{equation*} Lu=f \end{equation*}

where \(f\) is also analytic in \(\Omega\), then \(u\) is analytic in \(\Omega\). [1, Theorem 7.5.1]

Questions Link to heading

• Is \(\Omega\) just open?

References Link to heading

1. L. Hörmander, Linear partial differential operators. Berlin, Gottingen, Heidelberg, [Germany]: Springer-Verlag, 1963.