The aim of this note is to describe geometric conditions under which a Riemannian manifold enjoys the Feller property and to show how the validity of the Feller property in combination with stochastic completeness provides a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set.
Pacelli Bessa, G., Pigola, S., Setti, A. (2013). Stochastic properties of Riemannian manifolds and applications to PDE's. In M.A. Picardello (a cura di), Trends in Harmonic Analysis (pp. 381-398). Milano : Springer Verlag Mailand [10.1007/978-88-470-2853-1_14].
Stochastic properties of Riemannian manifolds and applications to PDE's
Pigola, S;
2013
Abstract
The aim of this note is to describe geometric conditions under which a Riemannian manifold enjoys the Feller property and to show how the validity of the Feller property in combination with stochastic completeness provides a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set.
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