Results 11 to 20 of about 33,013 (283)
Fractional Laplacian in Bounded Domains [PDF]
Physical Review E, 2007 The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces.
A. Böttcher +20 more
core +4 more sources
Maximum principles for Laplacian and fractional Laplacian with critical integrability
The Journal of Geometric Analysis, 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 +2 more sources
On fractional Laplacians – 3 [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2016 We investigate the role of the noncompact group of dilations in $\mathbb R^n$ on the difference of the quadratic forms associated to the fractional Dirichlet and Navier Laplacians. Then we apply our results to study the Brezis--Nirenberg effect in two families of noncompact boundary value problems involving the Navier-Laplacian.
MUSINA, Roberta, Nazarov, A. I.
openaire +5 more sources
Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Nonlinear Analysis, 2021 This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou +3 more
doaj +1 more source
Fractal and Fractional, 2023 The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
doaj +1 more source
On the Fractional Dunkl Laplacian
Fractional Calculus and Applied Analysis, 2022 In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem for the fractional Dunkl Laplacian as well.
Fethi Bouzeffour, Wissem Jedidi
openaire +3 more sources
Monotonicity results for the fractional p-Laplacian in unbounded domains
Bulletin of Mathematical Sciences, 2021 In this paper, we develop a direct method of moving planes in unbounded domains for the fractional p-Laplacians, and illustrate how this new method to work for the fractional p-Laplacians.
Leyun Wu, Mei Yu, Binlin Zhang
doaj +1 more source
Nonlinear Analysis, 2022 In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the relativistic Schrödinger operator (–Δ + m2)s and the tempered fractional Laplacian (Δ + λ)β/2, we consider a relativistic ...
Wenwen Hou, Lihong Zhang
doaj +1 more source
A priori estimates of solutions to nonlinear fractional Laplacian equation
Electronic Research Archive, 2023 In this paper, we focus on the research of a priori estimates of several types of semi-linear fractional Laplacian equations with a critical Sobolev exponent.
Tao Zhang , Tingzhi Cheng
doaj +1 more source
Fractional Laplacians on ellipsoids
Mathematics in Engineering, 2021 6 pictures, 27 ...
Abatangelo N., Jarohs S., Saldana A.
openaire +6 more sources