Results 21 to 30 of about 508,446 (306)
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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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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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 the Convergence Result of the Fractional Pseudoparabolic Equation
Journal of Mathematics, 2023 In this paper, we consider the nonlinear fractional Laplacian pseudoparabolic equation (NFLPPE). We mainly focus on the convergence of mild solutions with respect to the order of fractional Laplacian.
Nguyen Van Tien, Reza Saadati
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On critical Kirchhoff problems driven by the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2021 We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature.
Luigi Appolloni +2 more
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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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International Journal for Numerical Methods in Fluids, Volume 95, Issue 1, Page 143-175, January 2023., 2023 We present a new strong‐form meshless solver combined with the boundary condition‐enforced immersed boundary method for the numerical solution of the nonstationary, incompressible, viscous Navier–Stokes equations in their stream function‐vorticity (in 2D) and vector potential‐vorticity (in 3D) formulation.
George C. Bourantas +6 more
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An Extension Problem Related to the Fractional Laplacian [PDF]
, 2006 The operator square root of the Laplacian (− ▵)1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition.
L. Caffarelli, L. Silvestre
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Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains
Discrete and Continuous Dynamical Systems. Series A, 2021 In this paper, we first establish a narrow region principle for systems involving the fractional Laplacian in unbounded domains, which plays an important role in carrying on the direct method of moving planes.
Lingwei Ma, Zhenqiu Zhang
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