199 citations · 665 across the 32 of their papers we have counts for
27 papers · 1 filter
Quantization for Palais-Smale sequences of the Liouville functional on closed surfaces
Andrea Malchiodi, Francesco Malizia, Luca Martinazzi
In this paper we prove a quantization property for Palais-Smale sequences of functionals related to Liouville equations on compact surfaces. While these equations have been extensi…
Non-constancy and multiplicity of half-harmonic maps from intervals into the circle
Ali Hyder, Luca Martinazzi
We study one-dimensional half-harmonic maps from the real line into the circle with prescribed exterior data. We show that, for every positive integer , if two disjoint interval…
One-dimensional half-harmonic maps into the circle and their degree
Luca Martinazzi, Ali Hyder
Given a half-harmonic map minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setmi…
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…
Normal conformal metrics on with -curvature having power-like growth
Ali Hyder, Luca Martinazzi
Answering a question by M. Struwe (Vietnam J. Math. 2020) related to the blow-up behaviour in the Nirenberg problem, we show that the prescribed -curvature equation $$Δ^2 u=(1-|…