Results 41 to 50 of about 473,820 (257)
On fractional Laplacians $– 2$
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2016 For s > −1 we compare two natural types of fractional Laplacians (−\mathrm{\Delta })^{s} , namely, the “Navier” and the “Dirichlet” ones.
Roberta Musina, Alexander I. Nazarov
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The Spatially Variant Fractional Laplacian
Fractional Calculus and Applied Analysis, 2023 We introduce a definition of the fractional Laplacian $(-Δ)^{s(\cdot)}$ with spatially variable order $s:Ω\to [0,1]$ and study the solvability of the associated Poisson problem on a bounded domain $Ω$. The initial motivation arises from the extension results of Caffarelli and Silvestre, and Stinga and Torrea; however the analytical tools and approaches
Andrea N. Ceretani, Carlos N. Rautenberg
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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 existence of ground state solutions to critical growth problems nonresonant at zero
Comptes Rendus. Mathématique, 2021 We prove the existence of ground state solutions to critical growth $p$-Laplacian and fractional $p$-Laplacian problems that are nonresonant at zero.
Perera, Kanishka
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The Neumann problem for the fractional Laplacian: regularity up to the boundary [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if $u$ is a weak solution of $(-\Delta)^s u=f$ in $\Omega$, $\mathcal N_s u=0$ in $\Omega^c$, then $u$ is $C^\alpha$ up tp the ...
A. Audrito +2 more
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Remarks on the Generalized Fractional Laplacian Operator
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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A duality approach to the fractional Laplacian with measure data [PDF]
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like ( ) s v = in R N ; with vanishing conditions at innity. Here is a bounded Radon measure whose support is compactly contained in R N , N 2, and () s
K. Karlsen, Francesco Petitta, S. Ulusoy
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Small Order Asymptotics of the Dirichlet Eigenvalue Problem for the Fractional Laplacian [PDF]
Journal of Fourier Analysis and Applications, 2020 We study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian (-Δ)s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Pierre Aime Feulefack +2 more
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Overdetermined problems with fractional laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2015 Added a missing assumption (1.3) in Theorem 1.1 and Theorem 1.2, which is used in the proof of Lemma 4 ...
Fall, Mouhamed Moustapha, Jarohs, Sven
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Boundary value problems for the fractional Pauli operator: spectral methods and convergence analysis [PDF]
Mathematics and Computational SciencesThis paper investigates boundary value problems for the fractional Pauli operator on a finite square domain, addressing a significant gap in the literature where such problems have not been previously studied.
Yusif Gasimov, Aynura Aliyeva
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