We investigate a class of equations including generalized Monge--Ampere 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.
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G. Porru, S. Vernier-Piro, A. Safoui, Best Possible Maximum Principles for Fully Nonlinear Elliptic Partial Differential Equations. Z. Anal. Anwend. 25 (2006), no. 4, pp. 421–434DOI 10.4171/ZAA/1299