Hopf maximum principle revisited

Abstract

A weak version of Hopf maximum principle for elliptic equations in divergence form $$ \sum_{i,j=1}^N\partial_i(a_{ij}(x)\partial_ju)=0 $$ with Holder continuous coefficients $a_{ij}$ was shown in [3], in the two-dimensional case. It was also pointed out that this result could be extended to any dimension. The objective of the present note is to provide a complete proof of this fact, and to cover operators more general than the one studied in [3].

Keywords

• Maximum principle