This Sobolev function is continuous?

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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