Results 11 to 20 of about 5,262 (196)
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. The second one comes from looking at the classical fractional Laplacian as the mean value (in the sphere) of the 1-dimensional fractional Laplacians in ...
Julio D. Rossi, Jorge Ruiz-Cases
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A Generalized Fractional Laplacian [PDF]
, 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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Remarks on the Generalized Fractional Laplacian Operator [PDF]
Mathematics, 2019 The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions ...
Chenkuan Li +3 more
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Maximum Principles for Laplacian and Fractional Laplacian with Critical Integrability [PDF]
The Journal of Geometric Analysis, 2023 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider the critical cases for Laplacian with zero order term and first order term. It is well known that for the Laplacian with zero order term $-Δ+c(x)$ in $B_1$, $c(x)\in L^p(B_1)$($B_1\subset \mathbf{R}^n$), the critical case for
Congming Li, Yingshu Lü
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Transference of Fractional Laplacian Regularity [PDF]
, 2014 7 pages. To appear in Special Functions, Partial Differential Equations and Harmonic Analysis. Proceedings of the conference in honor of Calixto P. Calder\'on, Roosevelt University at Chicago, November 16-18, 2012. C. Georgakis, A. Stokolos and W. Urbina (eds)
Roncal, L., Stinga, P.R.
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Stability of nonlinear Dirichlet BVPs governed by fractional Laplacian. [PDF]
ScientificWorldJournal, 2014 We consider a class of partial differential equations with the fractional Laplacian and the homogeneous Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated ...
Bors D.
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The Dirichlet problem for the fractional laplacian [PDF]
, 2017 This thesis is an introduction to the fractional Sobolev spaces and the fractional Laplace operator. We define the fractional Sobolev spaces and give their properties by comparing them with the classical version of Sobolev spaces. After giving the motivation that comes from the random walk theory, we define the fractional Laplacian.
Alkın, Aykut
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Laplacian Fractional Revival on Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm to check this phenomenon and find the earliest time when it occurs.
Ada Chan +5 more
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Asymmetric critical fractional p-Laplacian problems [PDF]
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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On fractional Laplacians – 3 [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2016 We investigate the role of the noncompact group of dilations in $\mathbb R^n$ on the difference of the quadratic forms associated to the fractional Dirichlet and Navier Laplacians. Then we apply our results to study the Brezis--Nirenberg effect in two families of noncompact boundary value problems involving the Navier-Laplacian.
MUSINA, Roberta, Nazarov, A. I.
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