Fractional Laplacian: Pohozaev identity and nonexistence results

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WEAK AND VISCOSITY SOLUTIONS OF THE FRACTIONAL LAPLACE EQUATION (2014, background): “The converse of Theorem 1 holds true if f is smooth enough thanks to the regularity theory for viscosity solutions, see [10].”
On the spectrum of two different fractional operators (2014, unknown): “…delle Ricerche, Via Ferrata 1, 27100 Pavia, Italy (enrico@mat.uniroma3.it) (MS received 20 October 2012; accepted 22 May 2013) In this paper we deal with two non-local operators that are both well known and widely studied in the literature in connection with elliptic problems of fractional type.”
On Fractional Laplacians (2013, background): “In this case both the operators (−∆Ω) s N and (−∆Ω) s D were considered in many articles on semilinear equations, see for instance [2, 9, 11, 12, 13, 14, 17], and compared in [8], [15].”
The Pohozaev Identity for the Fractional Laplacian (2012, background): “As announced in [16], this is the main result of the present paper, and reads as follows.”