Let $\Omega \subset R^n $ $(n \geq 2) $ an open bounded domain with smooth boundary $u \in W^{ 1,p}(\Omega)\cap L^{\infty}(\Omega)$ ($p \geq 2$ fixed). Suppose that exist $M > 0$ such that
$$ \int_B |\nabla u| \ dx \leq Mr$$ for all ball $B \subset \Omega,$ where $r$ is the radius of the ball $B.$
From this can I say that $u$ is continuous?
Thanks in advance