Results 1 to 10 of about 473,820 (257)
The trace fractional Laplacian and the mid-range fractional Laplacian [PDF]
Nonlinear Analysis, 2023 In this paper we introduce two new fractional versions of the Laplacian. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian.
Julio D. Rossi, Jorge Ruiz-Cases
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Strong unique continuation for the higher order fractional Laplacian [PDF]
Mathematics in Engineering, 2019 In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators.
García-Ferrero, María-Ángeles +1 more
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Assessing Age-Associated Influences on Paramagnetic and Diamagnetic Susceptibility Maps in Postmortem Human Brains. [PDF]
NMR BiomedWe applied the APART‐QSM method to in situ postmortem MRI from 47 subjects (31–91 years) to assess age effects on paramagnetic and diamagnetic susceptibility. Diamagnetic susceptibility declined with age in basal ganglia, possibly reflecting shared biological factors.
de Azevedo JHM +7 more
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Mellin definition of the fractional Laplacian [PDF]
Fractional Calculus and Applied Analysis, 2023 It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is ...
G. Pagnini, Claudio Runfola
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Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions [PDF]
SIAM Journal on Numerical Analysis, 2022 In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac representation based on the Green function for the fractional Laplacian operator
Changtao Sheng, Bihao Su, Cheng-long Xu
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Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains [PDF]
Journal of Functional Analysis, 2021 We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order $s$ in bounded Lipschitz domains $\Omega$: \[ \begin{aligned} \|u\|_{\dot{B}^{s+r}_{2,\infty}(\Omega)} \le C \|f\|_{L^2 ...
J. P. Borthagaray, R. Nochetto
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On the fractional Laplacian of variable order [PDF]
Fractional Calculus and Applied Analysis, 2021 We present a novel definition of variable-order fractional Laplacian on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Eric F Darve +4 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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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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