Let $f\in L^m(\Omega)$ for some $m>1$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$ ($N\geq 2$). Consider the equation, $$ \Delta_p u=f(x) $$for $p=N$, then $u$ is bounded in $\Omega$. Moreover, $u$ is continuous upto the boundary. Can anyone help me with the solution of this one. I have got this question while going through the paper : Lemma 3.7 of the paper below https://link.springer.com/content/pdf/10.1007%2Fs00030-016-0361-6.pdf
Thank you very much.