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} …

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 …

arxiv:1307.1789v1 [math.AP] 6 Jul 2013 Page 1 arxiv:1307.1789v1 [math.AP] 6 Jul 2013 To
appear in Riv. Mat. Univ. Parma (NS) Giovanni Franzina and Giampiero Palatucci Fractional …

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In this article we extend the Sobolev spaces with variable exponents to include the fractional
case, and we prove a compact embedding theorem of these spaces into variable exponent …

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

We complete the local regularity program for weak solutions to linear parabolic nonlocal
equations with bounded measurable coefficients. Within the variational framework we prove …

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 …