6 papers
Fractional Hardy inequalities on open sets
Abdelrazek Dieb, Remi Yvant Temgoua
Let be a bounded open set of class in and . We study a family of fractional Hardy-type inequalities \begin{equation} \frac{c_{N,s…
A note on a Pohozaev identity for the fractional Green function
Abdelrazek Dieb, Isabella Ianni
We get a Pohozaev-type identity for the fractional Green function, which extends to the fractional setting a classical result by Brezis and Peletier. Our result complements with so…
Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems
Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña
We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains.…
Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods
Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña
We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asympto…
Attainability of the fractional Hardy constant with nonlocal mixed boundary conditions. Applications
Boumediene Abdellaoui, Ahmed Attar, Abdelrazek Dieb +1
The first goal of this paper is to study necessary and sufficient conditions to obtain the attainability of the \textit{fractional Hardy inequality } $$Λ_{N}\equivΛ_{N}(Ω):=\inf_{\…
A nonlocal concave-convex problem with nonlocal mixed boundary data
Boumediene Abdellaoui, Abdelrazek Dieb, Enrico Valdinoci
The aim of this paper is to study a nonlocal problem with a mixed Dirichlet-Neumann exterior condition. We prove existence, nonexistence and multiplicity of positive energy solutio…