We know that the Weak Maximum Principle and Strong Maximum Principle in every PDE book,such as Theorem 3.1 and Theorem 3.5 in David Dilbarg's book. But I never see a author give a nonconstant function as a example can attain it's interior maximum (also on boundary) for the weak principle maximum. Is the example so difficult that they don't provide it ? or the weak maximum principle is the same as the strong maximum principle. In brief, I want an elliptic operator that satisfies the weak maximum principle but not the strong one.