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 …

We study the regularity up to the boundary of solutions to the Dirichlet problem for the
fractional Laplacian. We prove that if u is a solution of (− Δ) su= g in Ω, u≡ 0 in R n\Ω, for …

This is the first of two articles dealing with the equation (− Δ) sv= f (v) in R n, with s∈(0, 1),
where (− Δ) s stands for the fractional Laplacian—the infinitesimal generator of a Lévy …

In this paper we survey some results on the Dirichlet problem \left{_u=g^Lu=f_inR^n\Ω^inΩ\
right. for nonlocal operators of the form Lu\left(x\right)=PVR^n\left{u\left(x\right) …

In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem (-Δ)^ su= f
(u)(-Δ) su= f (u) in Ω, u\equiv0 Ω, u≡ 0 in\mathbb R^ n \ Ω R n\Ω. Here, s ∈ (0, 1) s∈(0, 1) …

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 …

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 …

In this paper, we study the existence of multiple ground state solutions for a class of
parametric fractional Schrödinger equations whose simplest prototype is (-Δ)^ s u+ V (x) u= λ …

This is a unique book that provides a comprehensive understanding of nonlinear equations
involving the fractional Laplacian as well as other nonlocal operators. Beginning from the …

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-
linear problems involving the fractional Laplacian and arising in the framework of continuum …