JournalsrmiVol. 29, No. 4pp. 1437–1476

A general form of the weak maximum principle and some applications

  • Guglielmo Albanese

    Università degli Studi di Milano, Italy
  • Luis J. Alías

    Universidad de Murcia, Spain
  • Marco Rigoli

    Università di Milano, Italy
A general form of the weak maximum principle and some applications cover
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Abstract

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.

Cite this article

Guglielmo Albanese, Luis J. Alías, Marco Rigoli, A general form of the weak maximum principle and some applications. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1437–1476

DOI 10.4171/RMI/764