I'm trying to better understand the following argument:
The function $u$ is in $L^q(M)$ for some $q > 2^\star=\frac{2n}{n-2}$. By standard elliptic theory, the $u$ is in $C^{2,\theta}(M)$, $0 < \theta < 1$.
It appears at the end of page 11 of this article.
I'm trying to use, but without success, the Gagliardo-Nirenberg-Sobolev inequality.