The first model is based on Darcy's law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the
3. Relations between the nonlocal Laplacian and the fractional Laplacian In this section, we introduce the fractional Laplacian operator as a special case of the nonlocal operator L. Then, we show that for the special kernels given by (6) with σ=constant, the nonlocal operator L approaches...
where1<p<q<Nσ,σ∈(0,1)and(−Δ)pσ,(−Δ)qσare fractional Laplacian operators defined in the principle value sense. The existence results are obtained by combining the Galerkin approximation, Lebesgue and Sobolev spaces, the Young measures approach, and the assumption of growth conditio...
Abstract In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry. Previous article in issue Next article in issue Keywords Conformal geometry ...
In recent years, there has been a great deal of interest in using the fractional Laplacian operator to model diverse physical phenomena, such as anomalous ...
In the present paper, motivated by the above papers, we study the existence of weak solutions for problem (1.1) involving nonlocal fractional operator. It is worth noticing that there are a few authors addressing the fractional p-Laplacian problems by using the nonlinear alternative of Leray-Scha...
(2013) Eigenvalue of fractional differential equations with p- Laplacian operator Discrete Dynamics in Nature and Society 2013 article-id: 137890, 8 pp.W.Q. Wu and X.B. Zhou. Eigenvalue of Fractional Differential Equations with p-Laplacian Operator. Discrete Dyn. Nat. Soc., 3, 2013....
From the view point of mathematics, an important feature of the fractional Laplacian operator is its nonlocal property, which makes it more challenge than the classical Laplacian operator. Solutions of (1.1) are related to the existence of standing wave solutions to the following fractional ...
Lv, W: Solvability for discrete fractional boundary value problems with a p-Laplacian operator. Discrete Dyn. Nat. Soc. 2013, Article ID 679290 (2013)W. Lv, "Solvability for discrete fractional boundary value prob- lems with a p -laplacian operator," Discrete Dynamics in Nature and Society,...
3) Laplacian operator 拉普拉斯算子 1. A fourth order partial differential denoising method based on four directional Laplacian operator; 一个基于四方向的拉普拉斯算子的四阶偏微分去噪方法 2. This paper reviewed three image denoising methods based on PDE such as φ-function,divergence-based PDE and...