A new approach to Sobolev spaces and connections to $\mathbf\Gamma$-convergence

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Characterization of Sobolev and BV Spaces (2011, methodology): “The next two lemmata are due to an observation of Stein (see [15] or [70]), adapted to our setting.”
Anisotropic fractional Sobolev norms (2013, background): “Ponce [33] obtained several extensions of the results in [2], from which Theorem 1 can also be deduced if anisotropic s-seminorms are used.”
Fractional p-Laplacian evolution equations (2016, background): “Hence, by the results of [27] on the Γ–convergence of Ψ sn , and having in mind (7.”
Global H\"older regularity for the fractional $p$-Laplacian (2014, unknown): “ollowing the proof, we can ﬁnd a constant cN depending only on Nsuch that k(−∆)s puk∞ ≤ cN kukp−1 C2(RN) 1−s . This is in accordancewith the well known fact that (1−s)(−∆)s p → −∆p as s→ 1− (see e.g. [17]). Remark 2.14. Consider the class of functions L(Ω) = {u∈ fWs,p(Ω) : (−∆)s pu= fstrongly for so”