everyone. I am relatively new to PDE and I am self-studying. I am REALLY puzzled by the following statement in a book, so I come to ask for help. If $u$ is a solution of $\Delta u = f$ in $B_1(0)$, and $u=g$ on $\partial {B_1}(0)$, why the following statement is true?
There is a constant $C$, which only depends on $n$, such that $\max |u| \le C({\max _{\partial {B_1}(0)}}|g| + {\max _{{B_1}(0)}}|f|)$
Thank you so much!
I have not got a clue after one hour...