37 citations · 93 across the 11 of their papers we have counts for
14 papers
Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation
Azahara DelaTorre, Gabriele Mancini, Angela Pistoia
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval , under Dirichlet conditions in the…
Extremals for fractional Moser-Trudinger inequalities in dimension 1 via harmonic extensions and commutator estimates
Gabriele Mancini, Luca Martinazzi
We prove the existence of extremals for fractional Moser-Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the correspondi…
Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains
Massimo Grossi, Gabriele Mancini, Daisuke Naimen +1
In this work we study the existence of nodal solutions for the problem where is…
Local and nonlocal singular Liouville equations in Euclidean spaces
Ali Hyder, Gabriele Mancini, Luca Martinazzi
We study metrics of constant -curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation $$(-Δ)^\frac{n}{2}w=e^{nw}-cδ_{0} \t…
Glueing a peak to a non-zero limiting profile for a critical Moser-Trudinger equation
Gabriele Mancini, Pierre-Damien Thizy
Druet [6] proved that if is a sequence of Moser-Trudinger type nonlinearities with critical growth, and if solves $$ \begin{cases} &Δu =f_γ(x,u)\,,~~ u>0\text{…
Improved Adams-type inequalities and their extremals in dimension 2m
Azahara DelaTorre, Gabriele Mancini
In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space , where is any bounded, smooth, open subset o…
Non-existence of extremals for the Adimurthi-Druet inequality
Gabriele Mancini, Pierre-Damien Thizy
The Adimurthi-Druet [1] inequality is an improvement of the standard Moser-Trudinger inequality by adding a -type perturbation, quantified by , where is…
Uniform bounds for higher-order semilinear problems in conformal dimension
Gabriele Mancini, Giulio Romani
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-Δ)^m u=h(x,u)\quad&\mbox{in }Ω,\\ u=\partial_nu=\cdots=\p…
The Moser-Trudinger inequality and its extremals on a disk via energy estimates
Gabriele Mancini, Luca Martinazzi
We study the Dirichlet energy of non-negative radially symmetric critical points of the Moser-Trudinger inequality on the unit disc in , and prove that it expan…
Extremal Functions for Singular Moser-Trudinger Embeddings
Stefano Iula, Gabriele Mancini
We study Moser-Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson-Chang type estimate by means of Onofri's i…
Singular Liouville Equations on : Sharp Inequalities and Existence Results
Gabriele Mancini
We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singulariti…
A note on compactness properties of the singular Toda system
Luca Battaglia, Gabriele Mancini
In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, L…
Onofri-type inequalities for singular Liouville equations
Gabriele Mancini
We study the blow-up behaviour of minimizing sequences for the singular Moser-Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimat…
Remarks on the Moser-Trudinger inequality
Luca Battaglia, Gabriele Mancini
We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metr…