Variational problems with free boundaries for the fractional Laplacian

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Hitchhiker's guide to the fractional Sobolev spaces (2011, unknown): “, [18, 88, 13, 17, 78], etc.”
Boundary regularity for fully nonlinear integro-differential equations (2014, background): “Currently, these models have only been studied for the fractional Laplacian L = (−∆); see [14, 13] and references therein.”
Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity (2013, background): “Caffarelli et al [15, 16] investigated free boundary problems of a fractional Laplacian.”
Higher regularity of the free boundary in the elliptic Signorini problem (2014, methodology): “ being developed by De Silva and Savin [DSS12a,DSS12b,DSS14a]. In particular, in [DSS14a] they prove the C1regularity of C2;free boundaries in the thin analogue of Alt-Caarelli minimization problem [CRS10]. Their method is based on Schauder-type estimates rather than hodograph-Legendre transform use”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, background): “y have been diﬀusely studied by H. Alt, L. Caﬀarelli and A. Friedman in e.g. [1, 2]. In nonlocal settings, functionals of this kind have been considered by L. Caﬀarelli, J.-M. Roquejoﬀre and O. Savin [18]. 1.3. Strategy of the proof. Ourapproach tothe proofofthe regularity ofminimizers of the energy”