For a bounded smooth domain $\Omega$, let $H_2^{s}(\Omega)$ be the usual Sobolev space on $\Omega$.

Define $A:=\{f\in H_2^{s}(\Omega)| \lVert f\rVert_{L^p(\Omega)}=1\}$ where $2<p<2_{s}^*$.

Can we show $A$ is a $C^2$-Hilbert manifold since I need to use the Morse lemma?