Results 51 to 60 of about 393,013 (283)

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.
openaire   +4 more sources

Fractional Laplacian in conformal geometry [PDF]

Advances in Mathematics, 2011
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operators in conformal geometry.
González Nogueras, María del Mar, Chang, Sun-Yung Alice   +1 more
openaire   +5 more sources

Path Laplacians versus fractional Laplacians as nonlocal operators on networks

New Journal of Physics, 2021
Here we study and compare nonlocal diffusion processes on networks based on two different kinds of Laplacian operators. We prove that a nonlocal diffusion process on a network based on the path Laplacian operator always converges faster than the standard
Ernesto Estrada
doaj   +1 more source

Existence and Uniqueness of Solutions to Four-Point Impulsive Fractional Differential Equations with p-Laplacian Operator

Mathematics, 2022
In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class of four-point impulsive fractional differential equations with p-Laplacian operators are studied. In addition, three examples are given to justify
Limin Chu, Weimin Hu, Youhui Su, Yongzhen Yun   +3 more
doaj   +1 more source

User’s guide to the fractional Laplacian and the method of semigroups [PDF]

Fractional Differential Equations, 2018
The \textit{method of semigroups} is a unifying, widely applicable, general technique to formulate and analyze fundamental aspects of fractional powers of operators $L$ and their regularity properties in related functional spaces.
P. R. Stinga
semanticscholar   +1 more source

A restricted nonlocal operator bridging together the Laplacian and the fractional Laplacian [PDF]

Calculus of Variations and Partial Differential Equations, 2020
In this work we introduce volume constraint problems involving the nonlocal operator (-Δ)δs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
J. C. Bellido, A. Ortega
semanticscholar   +1 more source

Lower bounds for fractional Laplacian eigenvalues [PDF]

Communications in Contemporary Mathematics, 2014
In this paper, we investigate eigenvalues of fractional Laplacian (–Δ)α/2|D, where α ∈ (0, 2], on a bounded domain in an n-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which improves some results due to Yildirim Yolcu and Yolcu in [Estimates for the sums of eigenvalues of the fractional Laplacian on a ...
Lingzhong Zeng, He-Jun Sun, Guoxin Wei
openaire   +3 more sources

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
semanticscholar   +1 more source

C(sp²)─H Bond Activation with a Heterometallic Nickel-Aluminium Complex. [PDF]

Angew Chem Int Ed Engl
Despite the prevalence of Ni/Al catalysts for pyridine C─H functionalization, mechanistic details of such systems remain scarce. Herein, we present the discovery of PCy3‐catalyzed bond‐breaking and making processes that occur in the coordination sphere of a novel Ni─Al heterometallic complex.
Zurakowski JA, Stadler B, Drover MW, Crimmin MR.   +3 more
europepmc   +2 more sources

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, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton   +2 more
semanticscholar   +1 more source