21 citations · 51 across the 8 of their papers we have counts for
12 papers · 1 filter
A sharp Sobolev inequality on the Caffarelli-Kohn-Nirenberg hyperbolic space
Baptiste Devyver, Louis Dupaigne, Pierre-Damien Thizy
In the Euclidean space , the sharp classical Sobolev inequality is equivalent by conformal invariance to a Sobolev inequality on the hyperbolic space .…
A Symmetry problem for some quasi-linear equations in Euclidean space
Ramya Dutta, Pierre-Damien Thizy
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear -Laplace equations in Euclidean space by showing symmetry and uniqueness of posit…
Critical points of arbitrary energy for the Trudinger-Moser functional in planar domains
Andrea Malchiodi, Luca Martinazzi, Pierre-Damien Thizy
Given a smoothly bounded non-contractible domain , we prove the existence of positive critical points of the Trudinger-Moser embedding for arbitrary Dirichle…
Sign-changing blow-up for the Moser-Trudinger equation
Luca Martinazzi, Pierre-Damien Thizy, Jérôme Vétois
Given a sufficiently symmetric domain , for any and we construct blowing-up solutions $(u_\varepsilon)\subset H^1_0(Ω…
Critical points of the Moser-Trudinger functional on closed surfaces
Francesca De Marchis, Andrea Malchiodi, Luca Martinazzi +1
Given a closed Riemann surface and any positive smooth weight, we use a minmax scheme together with compactness, quantization results and with sharp energy estimates to pro…
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{…
When does a perturbed Moser-Trudinger inequality admit an extremal?
Pierre-Damien Thizy
In this paper, we are interested in several questions raised mainly in [17]. We consider the perturbed Moser-Trudinger inequality below, at the critical level , w…
Sharp quantization for Lane-Emden problems in dimension two
Pierre-Damien Thizy
In this short note, we prove a sharp quantization for positive solutions of Lane-Emden problems in a bounded planar domain. This result has been conjectured by De Marchis, Ianni an…
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…
Multi-bumps analysis for trudinger-moser nonlinearities i -quantification and location of concentration points
Olivier Druet, Pierre-Damien Thizy
In this paper, we investigate carefully the blow-up behaviour of sequences of solutions of some elliptic PDE in dimension two containing a nonlinearity with Trudinger-Moser growth.…
Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five
Pierre-Damien Thizy, Jérôme Vétois
We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension . Such a construction is already available in the lit…
Klein-Gordon-Maxwell equations in high dimensions
Pierre-Damien Thizy
We prove the existence of a mountain-pass solution and the a priori bound property for the electrostatic Klein-Gordon-Maxwell equations in high dimension.