Results 31 to 40 of about 5,095 (231)
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
openaire +3 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
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
doaj +1 more source
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 +1 more
openaire +5 more sources
On fractional $p$-Laplacian problems with weight [PDF]
Differential and Integral Equations, 2015 10 ...
Raquel Lehrer +2 more
openalex +6 more sources
Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions
Fractal and Fractional, 2021 The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian ...
Gábor Maros, Ferenc Izsák
doaj +1 more source
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
An extension problem for the CR fractional Laplacian [PDF]
Advances in Mathematics, 2014 We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.
Rupert L. Frank +3 more
openalex +6 more sources
Variational Inequalities for the Fractional Laplacian [PDF]
Potential Analysis, 2016 19 ...
MUSINA, Roberta +2 more
openaire +4 more sources
Mellin definition of the fractional Laplacian
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 applied to radial functions.
Gianni Pagnini, Claudio Runfola
openaire +3 more sources