Functional Spaces for the Theory of Elliptic Partial Differential Equations

By Françoise Demengel, Gilbert Demengel, R. Erné. 2012

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A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian (2016, background): “Further informations on fractional Sobolev spaces and many references may be found in [1, 11, 13, 18, 21].”
Approximation rates for neural networks with general activation functions (2019, background): “m and so we can assume without loss of generality that Ω is centered at 0. We also remark that the function f ∈ Hm(Ω)can always be extended in a continuous fashion to Hm(Rd)since ∂Ω is Lipschitz (see [3,11]), and thus the extension f e in the statement of the theorem certainly exists. Note that the ”
Fractional Sobolev spaces with variable exponents and fractional p(x)-Laplacians (2017, background): “For general theory of classical Sobolev spaces we refer the reader to [1, 5] and for the variable exponent case to [8].”