We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear
equations driven by nonlocal, possibly degenerate, integro-differential operators, whose …

We study the obstacle problem related to a wide class of nonlinear integro-differential
operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove …

We investigate some of the effects of the lack of compactness in the critical Folland-Stein-
Sobolev embedding in very general (possible non-smooth) domains, by proving via De …

NONLOCAL HARNACK INEQUALITY FOR FRACTIONAL ELLIPTIC EQUATIONS WITH
ORLICZ GROWTH 1. Introduction We investigate the following no Page 1 NONLOCAL …

The purpose of this paper is twofold: first we study an eigenvalue problem for the fractional p-
sub-Laplacian over the fractional Folland–Stein–Sobolev spaces on stratified Lie groups …

Optimal decay for solutions of nonlocal semilinear equations with critical exponent in
homogeneous groups Page 1 Proceedings of the Royal Society of Edinburgh, page 1 of 29 …

We deal with a wide class of generalized nonlocal-Laplace equations, so-called nonlocal-
Laplace equations, in the Heisenberg framework. Under natural hypotheses on the-function …

In this paper, we establish the sharp fractional subelliptic Sobolev inequalities and
Gagliardo-Nirenberg inequalities on stratified Lie groups. The best constants are given in …

We deal with a wide class of nonlinear nonlocal equations led by integro-differential
operators of order $(s, p) $, with summability exponent $ p\in (1,\infty) $ and differentiability …

We prove interior boundedness and H\"{o} lder continuity for the weak solutions of nonlocal
double phase equations in the Heisenberg group $\mathbb {H}^ n $. This solves a problem …