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) …

By virtue of barrier arguments we prove Cα-regularity up to the boundary for the weak
solutions of a non-local, non-linear problem driven by the fractional p-Laplacian operator …

Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …

We establish sharp regularity estimates for solutions to L u= f in Ω⊂ R n, L being the
generator of any stable and symmetric Lévy process. Such nonlocal operators L depend on …

We consider nonlinear diffusive evolution equations posed on bounded space domains,
governed by fractional Laplace-type operators, and involving porous medium type …

Free boundary problems are those described by PDEs that exhibit a priori unknown (free)
interfaces or boundaries. These problems appear in physics, probability, biology, finance, or …

We prove the W loc 2⁢ s, p local elliptic regularity of weak solutions to the Dirichlet problem
associated with the fractional Laplacian on an arbitrary bounded open set of ℝ N. The key …

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz–
Sobolev spaces in R n. An improved embedding with an Orlicz–Lorentz target space, which …

We study energy functionals obtained by adding a possibly discontinuous potential to an
interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that …

We study solutions to L u= f in Ω⊂ R n, being L the generator of any, possibly non-
symmetric, stable Lévy process. On the one hand, we study the regularity of solutions to L u …