Results 31 to 40 of about 473,820 (257)
Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Discrete and Continuous Dynamical Systems. Series A, 2021 In this paper, we first establish a narrow region principle for systems involving the fractional Laplacian in unbounded domains, which plays an important role in carrying on the direct method of moving planes.
Lingwei Ma, Zhenqiu Zhang
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Fractional Laplacians : A short survey
Discrete & Continuous Dynamical Systems - S, 2022 <p style='text-indent:20px;'>This paper describes the state of the art and gives a survey of the wide literature published in the last years on the fractional Laplacian. We will first recall some definitions of this operator in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-
Daoud, Maha, Laamri, El Haj
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Fractional Revival of Threshold Graphs Under Laplacian Dynamics
Discussiones Mathematicae Graph Theory, 2020 We consider Laplacian fractional revival between two vertices of a graph X. Assume that it occurs at time τ between vertices 1 and 2. We prove that for the spectral decomposition L=∑r=0qθrErL = \sum\nolimits_{r = 0}^q {{\theta _r}{E_r}} of the Laplacian
Kirkland Steve, Zhang Xiaohong
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Fractal and Fractional, 2022 This paper designs a new finite difference compact reconstruction unequal-sized weighted essentially nonoscillatory scheme (CRUS-WENO) for solving fractional differential equations containing the fractional Laplacian operator.
Yan Zhang, Jun Zhu
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User’s guide to the fractional Laplacian and the method of semigroups [PDF]
Fractional Differential Equations, 2018 The \textit{method of semigroups} is a unifying, widely applicable, general technique to formulate and analyze fundamental aspects of fractional powers of operators $L$ and their regularity properties in related functional spaces.
P. R. Stinga
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The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary [PDF]
, 2012 We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of ( − Δ ) s u = g in Ω, u ≡ 0 in R n \ Ω , for some s ∈ ( 0 , 1 ) and g ∈ L ∞ ( Ω ) , then u is C s ( R n ...
Xavier Ros-Oton, J. Serra
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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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Local energy estimates for the fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2020 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.
J. P. Borthagaray +2 more
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Communications in Partial Differential Equations, 2014 14 pages; this version is considerably ...
MUSINA, Roberta, Nazarov A. I.
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Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications [PDF]
, 2018 The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\mathbb{Z}_h\to\mathbb{R ...
Ciaurri, Ó. +4 more
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