Results 1 to 10 of about 508,408 (270)
The trace fractional Laplacian and the mid-range fractional Laplacian [PDF]
Nonlinear Anal, 247 (2024), Paper No. 113605, 24pp, 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
arxiv +6 more sources
Maximum principles for Laplacian and fractional Laplacian with critical integrability [PDF]
arXiv, 2019 In this paper, we study maximum principles for Laplacian and fractional Laplacian with critical integrability. We first consider $-\Delta u(x)+c(x)u(x)\geq 0$ in $B_1$ where $c(x)\in L^{p}(B_1)$, $B_1\subset \mathbf{R}^n$. As is known that $p=\frac{n}{2}$
Lü, Yingshu
core +3 more sources
Mellin definition of the fractional Laplacian [PDF]
Fractional Calculus and Applied Analysis, 2023 It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is ...
G. Pagnini, Claudio Runfola
semanticscholar +4 more sources
On the fractional Laplacian of variable order [PDF]
Fractional Calculus and Applied Analysis, 2021 We present a novel definition of variable-order fractional Laplacian on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Eric F Darve +4 more
semanticscholar +6 more sources
A Class of Fractional p-Laplacian Integrodifferential Equations in Banach Spaces [PDF]
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
doaj +2 more sources
The extremal solution for the fractional Laplacian [PDF]
Calculus of Variations and Partial Differential Equations, 2013 We study the extremal solution for the problem $(- )^s u= f(u)$ in $ $, $u\equiv0$ in $\R^n\setminus $, where $ >0$ is a parameter and $s\in(0,1)$. We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded
Xavier Ros‐Oton, Joaquim Serra
openalex +7 more sources
Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit [PDF]
arXiv, 2014 The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber $N$ of identical particles is introduced. We suggest a "fractional elastic harmonic potential", and obtain the $N$-periodic fractionalLaplacian
Collet, Bernard +3 more
core +1 more source
Point-like perturbed fractional Laplacians through shrinking potentials of finite range [PDF]
arXiv, 2018 We reconstruct the rank-one, singular (point-like) perturbations of the $d$-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr\"{o}dinger operators with regular potentials centred around the perturbation
Michelangeli, Alessandro +1 more
core +2 more sources
Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian [PDF]
Journal of Function Spaces and Applications, 2013 We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut ...
Ya-ling Li, Shi-you Lin
doaj +2 more sources
A new definition of the fractional Laplacian [PDF]
arXiv, 2002 It is noted that the standard definition of the fractional Laplacian leads to a hyper-singular convolution integral and is also obscure about how to implement the boundary conditions.
Chen, W.
core +2 more sources