We provide an overview of recent results concerning elliptic variational problems with
nonstandard growth conditions and related to different kinds of nonuniformly elliptic …

Minimizers of functionals of the type w ↦ ∫ Ω [ | D w | p - f w ] d x + ∫ R n ∫ R n | w ( x ) - w (
y ) | γ | x - y | n + s γ d x d y \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} …

We consider a combination of local and nonlocal $ p $-Laplace equations and discuss
several regularity properties of weak solutions. More precisely, we establish local …

In this note we present some of the most basic aspects of the fractional Laplacean with a self-
contained and purely didactic intent, and with a somewhat different slant from the several …

We consider equations involving a combination of local and nonlocal degenerate p-Laplace
operators. The main contribution of the paper is almost Lipschitz regularity for the …

We prove some regularity estimates for viscosity solutions to a class of possible degenerate
and singular integro-differential equations whose leading operator switches between two …

We prove higher Hölder regularity for solutions of equations involving the fractional p-
Laplacian of order s, when p≥ 2 and 0< s< 1. In particular, we provide an explicit Hölder …

We obtain nontrivial solutions to the Brezis–Nirenberg problem for the fractional p-Laplacian
operator, extending some results in the literature for the fractional Laplacian. The quasilinear …

We prove fine higher regularity results of Calderón-Zygmund-type for equations involving
nonlocal operators modelled on the fractional p-Laplacian with possibly discontinuous …

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 …