Spectral and stochastic properties of the $f$-Laplacian, solutions of PDE's at infinity, and geometric applications

Abstract

The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spectral theory and from a combination of stochastic properties of the relevant differential operators. Possible links between spectral and stochastic properties are analyzed in detail.

arXiv commentSlightly revised version. Corrected a few minor mistakes, references updated. To appear in: Rev. Mat. Iberoam