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.
Cite this article
G. Pacelli Bessa, Stefano Pigola, Alberto G. Setti, Spectral and stochastic properties of the -Laplacian, solutions of PDEs at infinity and geometric applications. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 579–610DOI 10.4171/RMI/731