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.
Stochastic properties of Riemannian manifolds and applications to PDE's
PIGOLA, STEFANO;SETTI, ALBERTO GIULIO
2013-01-01
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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