Results 11 to 20 of about 5,095 (231)
The extremal solution for the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2013 We study the extremal solution for the problem $(- )^s u= f(u)$ in $ $, $u\equiv0$ in $\R^n\setminus $, where $ >0$ is a parameter and $s\in(0,1)$. We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded
Xavier Ros‐Oton, Joaquim Serra
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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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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 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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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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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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Mathematical Methods in the Applied Sciences, EarlyView., 2022 This article focuses on the fully distributed leader‐following consensus problem of nonlinear fractional multi‐agent systems via event‐triggered control technique. The main intention of this article is to design a novel event‐triggered mechanism, which not only takes into account both the relative error and the absolute error of the samples but also ...
Qiaoping Li, Chao Yue
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