Layer solutions in a half‐space for boundary reactions

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On a Fractional Ginzburg–Landau Equation and 1/2-Harmonic Maps into Spheres (2013, methodology): “Using this lemma, it is then elementary to see that Ĥ1/2(ω;Rm) is a Hilbert space for the scalar product associated to the norm v 7→ ‖v‖L2(ω) + (E(v, ω))1/2.”
Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “equations, are now experiencing impressive applications in different subjects, such as, among others, the thin obstacle problem [87, 69], optimization [37], finance [26], phase transitions [2, 14, 88, 40, 45], stratified materials [83, 23, 24], anomalous diffusion [68, 98, 65], crystal dislocation [”
Nonlocal Equations with Measure Data (2014, methodology): “For instance, we mention their use in quasi-geostrophic dynamics [15], nonlocal diffusion and modified porous medium equations [10, 46, 47], dislocation problems [12], phase transition models [1, 11], image reconstruction problems [23].”
Gamma convergence of an energy functional related to the fractional Laplacian (2008, unknown): “Other works can be found in Cabré and Solá-Morales [8], where they look at layer solutions for boundary reactions of the half-Laplacian (s = 1/2).”
Uniqueness of Radial Solutions for the Fractional Laplacian (2013, methodology): “Inspired by the work of Cabré and Sire [9] (see also [10] for earlier work in the case s D 1 2 ) on layer and radial solutions of nonlinear equations of the form .”