# Boundary continuity of p-Laplace equation

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.