Maximum principles for P-Functions in elliptic partial differential equations

A function is said to satisfy a maximum principle in a domain Ω if the function either is constant or does not attain a maximum in Ω. Moreover, if Ω is a bounded domain, then a function which satisfies a maximum principle in Ω and which is continuous on Ω must attain its maximum value on ∂Ω Maximum principles are developed for certain P-functions; i.e., functions defined on solutions of an elliptic partial differential equation. In turn, these maximum principles are used to obtain information about solutions of some second order semilinear elliptic equations as well as solutions of higher order elliptic equations. Maximum principles for P-functions associated with a system of second order elliptic equations are also considered.