Keller-Osserman conditions for diffusion-type operators on Riemannian manifolds |
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Authors: | Luciano Mari |
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Affiliation: | a Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy b Dipartimento di Fisica e Matematica, Università dell'Insubria - Como, via Valleggio 11, I-22100 Como, Italy |
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Abstract: | In this paper we obtain essentially sharp generalized Keller-Osserman conditions for wide classes of differential inequalities of the form Lu?b(x)f(u)?(|∇u|) and Lu?b(x)f(u)?(|∇u|)−g(u)h(|∇u|) on weighted Riemannian manifolds, where L is a non-linear diffusion-type operator. Prototypical examples of these operators are the p-Laplacian and the mean curvature operator. The geometry of the underlying manifold is reflected, via bounds for the modified Bakry-Emery Ricci curvature, by growth conditions for the functions b and ?. A weak maximum principle which extends and improves previous results valid for the φ-Laplacian is also obtained. Geometric comparison results, valid even in the case of integral bounds for the modified Bakry-Emery Ricci tensor, are presented. |
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Keywords: | Keller-Osserman condition Diffusion-type operators Weak maximum principles Weighted Riemannian manifolds Quasi-linear elliptic inequalities |
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