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Zeitschrift für Analysis und ihre Anwendungen


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Volume 25, Issue 4, 2006, pp. 421–434
DOI: 10.4171/ZAA/1299

Published online: 2006-12-31

Best Possible Maximum Principles for Fully Nonlinear Elliptic Partial Differential Equations

G. Porru[1], A. Safoui[2] and S. Vernier-Piro[3]

(1) Università Studi Cagliari, Italy
(2) University of Marrakesh, Morocco
(3) Università Studi Cagliari, Italy

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.

Keywords: Fully nonlinear elliptic equations, Weingarten surfaces, best possible maximum principles

Porru G., Safoui A., Vernier-Piro S.: Best Possible Maximum Principles for Fully Nonlinear Elliptic Partial Differential Equations. Z. Anal. Anwend. 25 (2006), 421-434. doi: 10.4171/ZAA/1299