On the spectrum of two different fractional operators

By Raffaella Servadei, Enrico Valdinoci. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2014

282 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7df2003234c0531115c8563b63700d5a1213fa4a

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Citations in the corpus

The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator (2016, background): “We refer the interested reader to [20] for a careful comparison of theses two operator.”
On Fractional Laplacians (2013, background): “In this case both the operators (−∆Ω) s N and (−∆Ω) s D were considered in many articles on semilinear equations, see for instance [2, 9, 11, 12, 13, 14, 17], and compared in [8], [15].”
Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations (2015, background): “The first eigenvalue λ1(r) is characterized in the next lemma, which comprises results from [33] and [34] and clarifies the spectral properties of the fractional Laplacian.”
Global H\"older regularity for the fractional $p$-Laplacian (2014, methodology): “We refer the reader to [20] for a discussion on the comparison between the integral fractional laplacian and the regional (or spectral) notion obtained by taking the s-powers of the Laplacian operator −∆ with zero Dirichlet boundary conditions.”
The higher order fractional Calderón problem for linear local operators: Uniqueness (2020, methodology): “In particular, our global definition of the fractional Laplacian using Fourier transform will be different from the spectral definition used in [21] (see for example [13, 47]).”
Nonlocal Diffusion and Applications (2015, background): “27) By Theorem 4 of [85], we know that the functional G attains its minimum among all the functions u P W 1,1 loc pp0,`8qq X Cpr0,`8qq with up0q “ 1.”
Local Elliptic Regularity for the Dirichlet Fractional Laplacian (2017, background): “A direct proof that uk cannot be Lipschitz continuous up to the boundary is also contained in [28] and the references therein, where it has been shown that the eigenfunctions are s-Hölder continuous up to the boundary and this regularity is optimal.”
Nonhomogeneous boundary conditions for the spectral fractional Laplacian (2015, background): “in Bonforte, Sire and Vazquez [5], Grubb [15], Caffarelli and Stinga [7], Servadei and Valdinoci [18].”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “The difference between RFL and SFL seems to have been well-known to probabilists, it was discussed later in PDEs, see Servadei-Valdinoci [217], Bonforte and the author [51], and Musina-Nazarov [196].”