Revista Matemática Iberoamericana

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Volume 22, Issue 3, 2006, pp. 801–831
DOI: 10.4171/RMI/474

Published online: 2006-12-31

Some non-linear function theoretic properties of Riemannian manifolds

Stefano Pigola[1], Marco Rigoli[2] and Alberto G. Setti[3]

(1) Università dell'Insubria, Como, Italy
(2) Università di Milano, Italy
(3) Università dell'Insubria, Como, Italy

We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the $p$-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.

Keywords: Non-linear potential theory, p-Laplacian type operators, Riemannian manifolds

Pigola Stefano, Rigoli Marco, Setti Alberto: Some non-linear function theoretic properties of Riemannian manifolds. Rev. Mat. Iberoam. 22 (2006), 801-831. doi: 10.4171/RMI/474