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Fractional Laplacian in bounded domains [PDF]
Physical Review E, 2007 11 pages, 11 ...
Zoia, A., Rosso, A., Kardar, M.
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Fractional Laplacians : A short survey
Discrete and Continuous Dynamical Systems - S, 2022 The authors give an overview of the different operators which extend the Laplacian one to the fractional derivatives context. They concentrate on their very definitions and basic properties, stressing on some differences among them and the classical Laplacian, also by making use of explicit examples.
Daoud, Maha, Laamri, El Haj
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Communications in Partial Differential Equations, 2014 We compare two natural types of fractional Laplacians $(-Δ)^s$, "Navier" and "Dirichlet" ones.
MUSINA, Roberta, Nazarov A. I.
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A detour on a class of nonlocal degenerate operators
Bruno Pini Mathematical Analysis Seminar, 2023 We present some recent results on a class of degenerate operators which are modeled on the fractional Laplacian, converge to the truncated Laplacian, and are extremal among operators with fractional diffusion along subspaces of possibly different ...
Delia Schiera
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On the fractional p-Laplacian problems [PDF]
Journal of Inequalities and Applications, 2021 AbstractThis paper deals with nonlocal fractionalp-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractionalp-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next
Q-Heung Choi, Tacksun Jung
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On fractional Laplacians $– 2$
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2016 For s > −1 we compare two natural types of fractional Laplacians (−\mathrm{\Delta })^{s} , namely, the “Navier” and the “Dirichlet” ones.
Roberta Musina, Alexander I. Nazarov
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Local Energy Estimates for the Fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2021 The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the ...
Juan Pablo Borthagaray +2 more
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Remarks on the Generalized Fractional Laplacian Operator
Mathematics, 2019 The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions ...
Chenkuan Li +3 more
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On the existence of ground state solutions to critical growth problems nonresonant at zero
Comptes Rendus. Mathématique, 2021 We prove the existence of ground state solutions to critical growth $p$-Laplacian and fractional $p$-Laplacian problems that are nonresonant at zero.
Perera, Kanishka
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Variational Inequalities for the Fractional Laplacian [PDF]
Potential Analysis, 2016 19 ...
MUSINA, Roberta +2 more
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