Best possible maximum principles for fully nonlinear elliptic partial differential equations (Q873750)

Summary: We investigate a class of equations including generalized Monge--Ampère equations as well as Weingarten equations and prove a maximum principle for suitable functions involving the solution and its gradient. Since the functions which enjoy the maximum principles are constant for special domains, we have a so called best possible maximum principle that can be used to find accurate estimates for the solution of the corresponding Dirichlet problem. For these equations we also give a variational form which may have its own interest.