Revista Matemática Iberoamericana

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Volume 29, Issue 4, 2013, pp. 1437–1476
DOI: 10.4171/RMI/764

Published online: 2013-12-15

A general form of the weak maximum principle and some applications

Guglielmo Albanese[1], Luis J. Alías[2] and Marco Rigoli[3]

(1) Università degli Studi di Milano, Italy
(2) Universidad de Murcia, Spain
(3) Università di Milano, Italy

The aim of this paper is to introduce new forms of the weak and Omori–Yau maximum principles for linear operators, notably for trace type operators, and show their usefulness, for instance, in the context of PDEs and in the theory of hypersurfaces. In the final part of the paper we consider a large class of nonlinear operators and we show that our previous results can be appropriately generalized to this case.

Keywords: Omori–Yau maximum principle, weak maximum principle, trace type operators, Riemannian manifolds

Albanese Guglielmo, Alías Luis, Rigoli Marco: A general form of the weak maximum principle and some applications. Rev. Mat. Iberoamericana 29 (2013), 1437-1476. doi: 10.4171/RMI/764