Maximum and monotonicity principles for elliptic boundary value problems in partitioned domains

Abstract

This paper presents generalized maximum and monotonicity principles (Hopf[10],Collatz [4])in partitioned domains for continuous functions which are smooth in every subdomain and satisfy some elliptic differential inequalities and interface conditions. In physical problems such partitions arise in connection with certain discontinuities and inhomogeneities. Applications to free boundary problems are indicated