DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES

By A. Fiscella, Raffaella Servadei, Enrico Valdinoci. 2015

199 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ddab06f8ce64f670d149af42941ba0fca2af6448

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Citations in the corpus

Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent (2015, background): “By [18] we known that C∞ 0 (Ω) is a dense subset of X0 .”
A critical fractional equation with concave-convex power nonlinearities (2013, methodology): “…in Ω. .56) Following [29] it is easy to prove that X (Ω) could also be deﬁned as the closure of C ∞ (Ω) with respect to the X s (Ω) -norm (see also [24]) 0 0 0 Hence, applying [34, Theorem 1.5] we have that there exist an index set I ⊆ N , a sequence of points { x k } k ∈ I ⊂ Ω , and two sequences…”
Hölder regularity for nonlocal double phase equations (2019, methodology): “For this, some very important tools recently introduced in the nonlocal theory, as the celebrated Caffarelli-Silvestre s-harmonic extension [8], and other minor successful tricks, as for instance the pseudo-differential commutator compactness in [31] or the energy density estimates in [10,19,32], se”
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “ng by a test function and integrating by parts the Laplacian term. Namely, consider the space V= {u∈ Hs(Rn) : u= 0 in Ωc}, equipped with the Hs(Rn) norm. For Vit is known that C∞ 0 (Ω) is a dense set [21]. Then, the weak formulation of (1.3) is: ﬁnd u∈ Vsuch that (2.1) C(n,s) 2 ¨ Q (u(x) −u(y))(v(x)”
Local Elliptic Regularity for the Dirichlet Fractional Laplacian (2017, background): “here is no obvious inclusion between Ws,p 0 (Ω) and W s,p 0 (Ω). In fact, for an arbitrary bounded open set Ω ⊂ RN, the two spaces are diﬀerent, since D(Ω) is not always dense in Ws,p 0 (Ω) (see e.g. [11]). But if Ω has a continuous boundary, then by [11, Theorem 6], D(Ω) is dense in Ws,p 0 (Ω) and ”
Degenerate Kirchhoff-type diffusion problems involving the fractional p-Laplacian (2017, background): “In this section, we first recall some definitions and properties of the fractional Sobolev spaces, see [9, 22, 35] for further details.”