Results 21 to 30 of about 473,820 (257)
What is the fractional Laplacian? A comparative review with new results [PDF]
Journal of Computational Physics, 2018 The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the ...
Anna Lischke +10 more
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On the Fractional Dunkl Laplacian
Fractional Calculus and Applied Analysis, 2022 In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem for the fractional Dunkl Laplacian as well.
Fethi Bouzeffour, Wissem Jedidi
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Fractal and Fractional, 2023 Recent studies have emphasized the importance of the long-distance diffusion model in characterizing tracer transport occurring within both subsurface and surface environments, particularly in heterogeneous systems.
Zhipeng Li +5 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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Asymmetric critical fractional p-Laplacian problems
Electronic Journal of Differential Equations, 2017 We consider the asymmetric critical fractional p-Laplacian problem $$\displaylines{ (-\Delta)^s_p u = \lambda |u|^{p-2} u + u^{p^\ast_s - 1}_+,\quad \text{in } \Omega;\cr u = 0, \quad \text{in } \mathbb{R}^N\setminus\Omega; }$$ where $\lambda>0 ...
Li Huang, Yang Yang
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Boundary Value Problems, 2021 We investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obtain these results by direct computations with
Q-Heung Choi, Tacksun Jung
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A Monotone Discretization for the Fractional Obstacle Problem and Its Improved Policy Iteration
Fractal and Fractional, 2023 In recent years, the fractional Laplacian has attracted the attention of many researchers, the corresponding fractional obstacle problems have been widely applied in mathematical finance, particle systems, and elastic theory.
Rubing Han, Shuonan Wu, Hao Zhou
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Monotone iterative technique for time-space fractional diffusion equations involving delay
Nonlinear Analysis, 2021 This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of ...
Qiang Li, Guotao Wang, Mei Wei
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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 ...
Zoia, A., Rosso, A., Kardar, M.
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