Quasilinear elliptic inequalities on complete Riemannian manifolds |
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| Authors: | Paolo Antonini Dimitri Mugnai Patrizia Pucci |
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| Affiliation: | aDipartimento di Matematica “Guido Castelnuovo”, “Sapienza” Università di Roma, P.le Aldo Moro 2, 00185 Roma, Italy;bDipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy |
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| Abstract: | 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. |
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| Keywords: | Singular and degenerate elliptic inequalities on manifolds Comparison principles |
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