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For a nonnegative function $f\in L^1(\Omega)$, where $\Omega$ is abounded smooth domain in $\mathbb{R}^N$, consider for $p=N$, the p-Laplace equation $-\Delta_p u=f$ in $\Omega$ such that $u\in W_{0}^{1,p}(\Omega)$.

Let $f\in L^m(\Omega)$ for some $m>1$, then $u\in C_{0}(\overline{\Omega})$. I am not getting how to prove this fact.

Please help me. Thanks.

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