刊名:Annales de l'Institut Henri Poincare (C) Non Linear Analysis
出版年:2016
出版时间:March-April 2016
年:2016
卷:33
期:2
页码:477-493
全文大小:362 K
文摘
We prove that for every p>1 and for every potential V∈Lp, any nonnegative function satisfying −Δu+Vu≥0 in an open connected set of RN is either identically zero or its level set {u=0} has zero W2,p capacity. This gives an affirmative answer to an open problem of Bénilan and Brezis concerning a bridge between Serrin–Stampacchia's strong maximum principle for and Ancona's strong maximum principle for p=1. The proof is based on the construction of suitable test functions depending on the level set {u=0}, and on the existence of solutions of the Dirichlet problem for the Schrödinger operator with diffuse measure data.