# Extremal functions for singular Moser-Trudinger embeddings

Iula, Stefano and Mancini, Gabriele. (2016) Extremal functions for singular Moser-Trudinger embeddings. Preprints Fachbereich Mathematik, 2016 (01).

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Official URL: https://edoc.unibas.ch/69957/

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 inequality for the unit disk in $\mathbb{R}^2$. Moreover we extend the analysis of [1] and [8] considering Adimurthi-Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals.