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papers

Publications (32)

math.AP2019

On $S U (3)$ Toda system with multiple singular sources

Ali Hyder, Chang-Shou Lin, Juncheng Wei

We consider the singular $S U (3)$ Toda system with multiple singular sources \begin{align*} \left\{\begin{array}{ll}-Îw_1=2e^{2w_1}-e^{w_2}+2Ï\sum_{\ell=1}^mÎ²_{1,\ell}Î´_{P_{\ell…

math.AP2015

Moser functions and fractional Moser-Trudinger type inequalities

Ali Hyder

We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimu…

math.AP2023

Blow-up Analysis of Stationary Solutions to a Liouville-Type Equation in 3-D

Francesca Da Lio, Ali Hyder

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation $- I^ u = e^{u} in I^c ◯$ , where $I^c ◯$ is an open set…

math.AP2020

Removability of singularities and superharmonicity for some fractional Laplacian equations

Weiwei Ao, Maria del Mar Gonzalez, Ali Hyder +1

We study some qualitative properties (including removable singularities and superharmonicity) of non-negative solutions to $(- I^)^{3} u = f u^{p} in R^{n} ∖ I^£$ …

math.AP2019

Gluing metrics with prescribed $Q$ -curvature and different asymptotic behaviour in high dimension

Ali Hyder, Luca Martinazzi

We show a new example of blow-up behaviour for the prescribed $Q$ -curvature equation in even dimension $6$ and higher, namely given a sequence $(V_{k}) \subset C^{0} (R^{2 n})$ s…

math.AP2025

One-dimensional half-harmonic maps into the circle and their degree

Luca Martinazzi, Ali Hyder

Given a half-harmonic map $u \in H ˙^{\frac{1}{2}, 2} (R, S^{1})$ minimizing the fractional Dirichlet energy under Dirichlet boundary conditions in $\mathbb{R}\setmi…