We describe the mathematical theory of diffusion and heat transport with a view to including
some of the main directions of recent research. The linear heat equation is the basic …

In this paper, we consider the fractional Laplacian-(-Δ) α/2 on an open subset in ℝ_d_ with
zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such …

In this paper, we develop a novel finite difference method to discretize the fractional
Laplacian (− Δ) α/2 in hypersingular integral form. By introducing a splitting parameter, we …

This paper describes the state of the art and gives a survey of the wide literature published
in the last years on the fractional Laplacian. We will first recall some definitions of this …

In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian,
spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These …

We provide a quantitative study of nonnegative solutions to nonlinear diffusion equations of
porous medium-type of the form∂ t u+ ℒ um= 0, m> 1, where the operator ℒ belongs to a …

Suppose that d\geq2 and α∈(1,2). Let D be a bounded C^1,1 open set in R^d and b an R^d-
valued function on R^d whose components are in a certain Kato class of the rotationally …

Regularity results for stable-like operators Page 1 Journal of Functional Analysis 257 (2009)
2693–2722 www.elsevier.com/locate/jfa Regularity results for stable-like operators ✩ Richard …

We investigate quantitative properties of nonnegative solutions u (t, x)≥ 0 to the nonlinear
fractional diffusion equation,∂ t u+ LF (u)= 0 posed in a bounded domain, x∈ Ω⊂ RN, with …

We survey recent regularity results for parabolic equations involving nonlocal operators like
the fractional Laplacian. We extend the results of Felsinger-Kassmann (2013) and obtain …