Global Heat Kernel Estimates for Fractional Laplacians in Unbounded Open Sets [PDF]
, 2009 In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two classes of unbounded C^{1,1} open sets in R^d: half-space-like open sets ...
Chen, Zhen-Qing, Tokle, Joshua
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Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications [PDF]
Computer Methods in Applied Mechanics and Engineering, 2018 In this paper, we propose accurate and efficient finite difference methods to discretize the two- and three-dimensional fractional Laplacian ( − Δ ) α 2 ( 0 α 2 ) in hypersingular integral form.
Siwei Duo, Yanzhi Zhang
semanticscholar +1 more source
Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules [PDF]
, 2015 It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzmann equation enjoys similar regularity properties as the heat equation with ...
Barbaroux, Jean-Marie +3 more
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Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains [PDF]
SIAM Journal on Numerical Analysis, 2019 In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving integral fractional Laplacian in $\mathbb{R}^d$, which is built upon two essential components: (i) the Dunford-Taylor formulation of the fractional Laplacian; and (ii ...
Changtao Sheng +4 more
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A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces
Abstract and Applied Analysis, 2013 We study a class of nonlinear fractional integrodifferential equations with p-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractional p-Laplacian equations ...
Yiliang Liu, Liang Lu
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Local Elliptic Regularity for the Dirichlet Fractional Laplacian [PDF]
, 2017 We prove the Wloc2s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consists in analyzing
U. Biccari, M. Warma, E. Zuazua
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Numerical approximation of the integral fractional Laplacian [PDF]
Numerische Mathematik, 2017 We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem.
A. Bonito, Wenyu Lei, J. Pasciak
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Fractional discrete Laplacian versus discretized fractional Laplacian
, 2015 25 pages, 13 ...
Ciaurri, Ó. +4 more
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Local convergence of the FEM for the integral fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2020 We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm.
M. Faustmann, M. Karkulik, J. Melenk
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Transference of Fractional Laplacian Regularity [PDF]
, 2014 In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus $\mathbb{T}^n$ from the fractional Laplacian on $\mathbb{R}^n$. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that $L^2$ functions on the torus can not be identified
Roncal, L., Stinga, P.R.
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