Quasilinear elliptic inequalities on complete Riemannian manifolds
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چکیده
We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some related boundary value problems are presented. © 2007 Elsevier Masson SAS. All rights reserved. Résumé Nous démontrons des principes de maximum et de comparaison pour les solutions distributionnelles faibles d’inégalités différentielles quasi-linéaires elliptiques, éventuellement singulières ou dégénérées, sous forme divergence sur les variétés riemanniennes complètes. On présente une nouvelle définition d’ellipticité pour les opérateurs non-linéaires sur des variétés riemanniennes, en couvrant les exemples importants standards. Comme application, nous présentons quelques résultats d’unicité pour des problèmes aux limites. © 2007 Elsevier Masson SAS. All rights reserved. MSC: primary 58J05, 58J32; secondary 35B50
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تاریخ انتشار 2006