We assumed that $\Omega_0 \subset \mathbb{R}^2$ is a simple connected bounded domain, $\Gamma = \partial \Omega_0$ is a smooth curve. $u \in H^3(\Omega_0)$ and $\|\partial^{\alpha}u\|_{L^{\infty}(\Gamma)}<\infty,|\alpha|\leq 2$.
Because of Sobolev Embedding Theorem, we know that $u \in W^{1,\infty}(\Omega_0)$, but i don't know that whether $u \in W^{2,\infty}(\Omega_0)$ or not. if not, i want to know in which condition it is true.