Stable Solutions of Elliptic Partial Differential Equations

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Partial regularity of finite Morse index solutions to the Lane–Emden equation (2011, background): “Some well-known ingredients Proofs of all the results in this section can be found in [9].”
Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ (2019, background): “11) can be summarized as follows (see for instance [4, Theorem 1 and Remark 1] or the book [21] by Dupaigne): Theorem 1.”
The extremal solution for the fractional Laplacian (2013, background): “It is well known —see [4] or the excellent monograph [16] and references therein— that in the classical case s = 1 there exists a finite extremal parameter λ∗ such that if 0 < λ < λ∗ then problem (1.”