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.
Pacelli Bessa, G., Pigola, S., Setti, A. (2013). Spectral and stochastic properties of the f-Laplacian, solutions of PDE's at infinity and geometric applications. REVISTA MATEMATICA IBEROAMERICANA, 29(2), 579-610 [10.4171/rmi/731].
Spectral and stochastic properties of the f-Laplacian, solutions of PDE's at infinity and geometric applications
Stefano Pigola
;
2013
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.
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