Results 61 to 70 of about 101,180 (174)
A note on the existence and multiplicity of solutions for sublinear fractional problems
Boundary Value Problems, 2017 In this paper, we study the existence of weak solutions for fractional p-Laplacian equations with sublinear growth and oscillatory behavior as the following L K p u = λ f ( x , u ) in Ω , u = 0 in R N ∖ Ω , $$ \begin{aligned} &\mathcal{L}^{p}_{K}u ...
Yongqiang Fu
doaj +1 more source
The eigenvalue problem for the regional fractional Laplacian in the small order limit [PDF]
arXiv, 2021 In this note, we study the asymptotic behavior of eigenvalues and eigenfunctions of the regional fractional Laplacian $(-\Delta)^s$ as $ s \to 0^+$. Our analysis leads to a study of the regional logarithmic Laplacian, which arises as a formal derivative of regional fractional Laplacians at $s = 0$.
arxiv
The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations [PDF]
Discrete and Continuous Dynamical Systems Series B, 2021, 2019 In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posedness of fractional-type anomalous unidirectional diffusion equations. This study is an extension of the work by Akagi-Kimura (2019) for the standard Laplacian. However, there
arxiv +1 more source
Laplacian pretty good fractional revival [PDF]
Discrete Mathematics (2022), 345(10), 112971, 2020 We develop the theory of pretty good fractional revival in quantum walks on graphs using their Laplacian matrices as the Hamiltonian. We classify the paths and the double stars that have Laplacian pretty good fractional revival.
arxiv +1 more source
A pointwise inequality for fractional laplacians
Advances in Mathematics, 2015 The fractional laplacian is an operator appearing in several evolution models where diffusion coming from a L vy process is present but also in the analysis of fluid interphases. We provide an extension of a pointwise inequality that plays a r le in their study. We begin recalling two scenarios where it has been used.
Cordoba Barba, Antonio +1 more
openaire +4 more sources
Maximum Principles for Laplacian and Fractional Laplacian with Critical Integrability
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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Fractional Laplacian with Hardy potential [PDF]
Communications in Partial Differential Equations, 2019 small editorial changes, added literature, new title, 28 pages, 1 ...
Krzysztof Bogdan +3 more
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Fractional discrete Laplacian versus discretized fractional Laplacian
, 2015 25 pages, 13 ...
Ciaurri, Ó. +4 more
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The parabolic p-Laplacian with fractional differentiability [PDF]
IMA Journal of Numerical Analysis, 2020 Abstract We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space–time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiǐ spaces and therefore cover situations when the (gradient of the) solution has only fractional ...
Breit, Dominic +3 more
openaire +5 more sources