The purpose of these pages is to collect a set of notes that are a result of several talks and
minicourses delivered here and there in the world (Milan, Cortona, Pisa, Roma, Santiago del …

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} …

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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 …

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 …

We consider the eigenvalue problem for the fractional p-Laplacian in an open bounded,
possibly disconnected set Ω⊂ ℝ n, under homogeneous Dirichlet boundary conditions. After …

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 …

These are the handouts of an undergraduate minicourse at the Università di Bari (see Fig.
1), in the context of the 2017 INdAM Intensive Period “Contemporary Research in elliptic …

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 …

The main goal of this work is to study existence, uniqueness and summability of the solution
u with respect to the summability of the datum f. In the process we establish an Lp-theory, for …