Results 11 to 20 of about 393,013 (283)
A Fractional Graph Laplacian Approach to Oversmoothing [PDF]
Neural Information Processing Systems, 2023 Graph neural networks (GNNs) have shown state-of-the-art performances in various applications. However, GNNs often struggle to capture long-range dependencies in graphs due to oversmoothing.
Sohir Maskey +3 more
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Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Nonlinear Analysis, 2021 This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou +3 more
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Fractal and Fractional, 2023 The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
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Fractional Laplacians on ellipsoids
Mathematics in Engineering, 2021 6 pictures, 27 ...
Abatangelo N., Jarohs S., Saldana A.
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Monotonicity results for the fractional p-Laplacian in unbounded domains
Bulletin of Mathematical Sciences, 2021 In this paper, we develop a direct method of moving planes in unbounded domains for the fractional p-Laplacians, and illustrate how this new method to work for the fractional p-Laplacians.
Leyun Wu, Mei Yu, Binlin Zhang
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Nonlinear Analysis, 2022 In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the relativistic Schrödinger operator (–Δ + m2)s and the tempered fractional Laplacian (Δ + λ)β/2, we consider a relativistic ...
Wenwen Hou, Lihong Zhang
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Nonradiality of second eigenfunctions of the fractional Laplacian in a ball [PDF]
Proceedings of the American Mathematical Society, 2021 Using symmetrization techniques, we show that, for every N ≥ 2 N \geq 2 , any second eigenfunction of the fractional Laplacian in the N N -dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its ...
Jivr'i Benedikt +3 more
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On fractional Laplacians – 3 [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 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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A priori estimates of solutions to nonlinear fractional Laplacian equation
Electronic Research Archive, 2023 In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent.
Tao Zhang , Tingzhi Cheng
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The Fractional Laplacian with Reflections
Potential Analysis, 2023 AbstractMotivated by the notion of isotropic $$\alpha $$ α -stable Lévy processes confined, by reflections, to a bounded open Lipschitz set $$D\subset \mathbb {R}^d$$ D ⊂ R
Bogdan, Krzysztof, Kunze, Markus
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