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Fractional Laplacian in bounded domains [PDF]
Physical Review E, 2007 11 pages, 11 ...
Andrea Zoia +3 more
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Fractional Laplacians : A short survey [PDF]
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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Communications in Partial Differential Equations, 2014 14 pages; this version is considerably ...
MUSINA, Roberta, Nazarov A. I.
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On the Fractional Dunkl Laplacian
, 2022 In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem for the fractional Dunkl Laplacian as well.
Fethi Bouzeffour, Wissem Jedidi
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The Pohozaev Identity for the Fractional Laplacian [PDF]
Archive for Rational Mechanics and Analysis, 2014 In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem $(- )^s u = f(u)$ in $ $, $u \equiv 0$ in $\mathbb R^n\setminus $. Here, $s\in(0,1)$, $(- )^s$ is the fractional Laplacian in $\mathbb R^n$, and $ $ is a bounded $C^{1,1}$ domain. To establish the identity we use, among other things, that if $u$ is a bounded solution
Ros Oton, Xavier +1 more
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The Spatially Variant Fractional Laplacian
Fractional Calculus and Applied Analysis, 2023 We introduce a definition of the fractional Laplacian $(-Δ)^{s(\cdot)}$ with spatially variable order $s:Ω\to [0,1]$ and study the solvability of the associated Poisson problem on a bounded domain $Ω$. The initial motivation arises from the extension results of Caffarelli and Silvestre, and Stinga and Torrea; however the analytical tools and approaches
Andrea N. Ceretani, Carlos N. Rautenberg
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Laplacian Fractional Revival on Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs.
Zhanghan Yin +5 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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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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Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions
Fractal and Fractional, 2021 The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian ...
Gábor Maros, Ferenc Izsák
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