This article discusses several definitions of the fractional Laplace operator L=—(—Δ) α/2 in
R d, also known as the Riesz fractional derivative operator; here α∈(0, 2) and d≥ 1. This is …

We report on recent progress in the study of nonlinear diffusion equations involving
nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous …

This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …

The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension
problem to the upper half space. In this paper we prove the same type of characterization for …

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the
Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive …

The content of this paper is at the interplay between function spaces Lp (x) and Wk, p (x) with
variable exponents and fractional Sobolev spaces Ws, p. We are concerned with some …

The regularity theory of free boundaries flourished during the late 1970s and early 1980s
and had a major impact in several areas of mathematics, mathematical physics, and …

Fractional Laplacian in conformal geometry Page 1 Advances in Mathematics 226 (2011)
1410–1432 www.elsevier.com/locate/aim Fractional Laplacian in conformal geometry Sun-Yung …

We present three schemes for the numerical approximation of fractional diffusion, which
build on different definitions of such a non-local process. The first method is a PDE approach …

This paper focuses on the following scalar field equation involving a fractional Laplacian:(−)
αu= g (u) in RN, where N⩾ 2, α∈(0, 1),(−) α stands for the fractional Laplacian. Using some …