I was asked to determine for which $u$ is there a classical solution to $\Delta u = f$ with $f\in H^m(\Omega)$ with $\Omega$ bounded, open with an infinitely smooth boundary?
I think that this follows from the $L^2$ regularity theory of elliptic problems and i answered with $u$ being a weak solution of the problem and $u\in H^{m+2}(\Omega)$.
Is this correct?
Thank you so much for your time.