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Maximum principles for Laplacian and fractional Laplacian with critical integrability
The Journal of Geometric Analysis, 2019 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider $-\Delta u(x)+c(x)u(x)\geq 0$ in $B_1$ where $c(x)\in L^{p}(B_1)$, $B_1\subset \mathbf{R}^n$. As is known that $p=\frac{n}{2}$
Lü, Yingshu
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On the fractional Laplacian of variable order [PDF]
Fractional Calculus and Applied Analysis, 2022 Abstract We present a novel definition of variable-order fractional Laplacian on $${\mathbb {R}}^n$$ R n
Darve, Eric +4 more
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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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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.
MUSINA, Roberta, Nazarov, Alexander I.
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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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Fractional Laplacian pyramids [PDF]
2009 16th IEEE International Conference on Image Processing (ICIP), 2009 We provide an extension of the L 2 -spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyharmonic splines to derive an efficient, non-separable filterbank implementation.
Delgado-Gonzalo, Ricard +2 more
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On comparison of fractional Laplacians [PDF]
Nonlinear Analysis, 2022 For $s>-1$, $s\notin\mathbb N_0$, we compare two natural types of fractional Laplacians $(- )^s$, namely, the restricted Dirichlet and the spectral Neumann ones. We show that for the quadratic form of their difference taken on the space $\tilde{H}^s( )$ is positive or negative depending on whether the integer part of $s$ is even or odd.
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Fractional Laplacian on the torus [PDF]
Communications in Contemporary Mathematics, 2016 We study the fractional Laplacian [Formula: see text] on the [Formula: see text]-dimensional torus [Formula: see text], [Formula: see text]. First, we present a general extension problem that describes any fractional power [Formula: see text], [Formula: see text], where [Formula: see text] is a general nonnegative self-adjoint operator defined in an ...
Pablo Raúl Stinga, Luz Roncal
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A Generalized Fractional Laplacian
, 2023 In this article we show that the fractional Laplacian in $R^{2}$ can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. Using this factored form we introduce a generalization of the fractional Laplacian, involving a matrix $K(x)$, suitable when the fractional Laplacian is applied in a non ...
Zheng, Xiangcheng +2 more
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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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