The purpose of these pages is to collect a set of notes that are a result of several talks and
minicourses delivered here and there in the world (Milan, Cortona, Pisa, Roma, Santiago del …

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 …

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian Page 1
Proceedings of the Royal Society of Edinburgh, 142A, 1237–1262, 2012 Positive solutions of …

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 …

arXiv:0901.3261v1 [math.PR] 21 Jan 2009 Page 1 arXiv:0901.3261v1 [math.PR] 21 Jan 2009
FROM THE LONG JUMP RANDOM WALK TO THE FRACTIONAL LAPLACIAN ENRICO …

Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative
properties of solutions Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL …

We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the
lattice h Z with mesh size h> 0. In the continuum limit when h→ 0, we prove that the limiting …

The main goal of this work is to study existence, uniqueness and summability of the solution
u with respect to the summability of the datum f. In the process we establish an Lp-theory, for …

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied
in this paper. By using an Almgren type monotonicity formula, separation of variables, and …

In this paper we study a class of fractional elliptic problems of the form where s∈(0, 1). We
prove nonexistence of positive solutions when Ω is star-shaped and f is supercritical. We …