Revista Matemática Iberoamericana


Full-Text PDF (368 KB) | Metadata | Table of Contents | RMI summary
Volume 29, Issue 2, 2013, pp. 579–610
DOI: 10.4171/RMI/731

Published online: 2013-04-22

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

G. Pacelli Bessa[1], Stefano Pigola[2] and Alberto G. Setti[3]

(1) Universidade Federal do Ceará, Fortaleza, Brazil
(2) Università dell'Insubria, Como, Italy
(3) Università dell'Insubria, Como, Italy

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

Keywords: Weighted Laplacians, Feller property, stochastic completeness, essential spectrum, gradient Ricci solitons

Bessa G. Pacelli, Pigola Stefano, Setti Alberto: Spectral and stochastic properties of the $f$-Laplacian, solutions of PDEs at infinity and geometric applications. Rev. Mat. Iberoamericana 29 (2013), 579-610. doi: 10.4171/RMI/731