Extremal Functions for Singular Moser-Trudinger Embeddings

Abstract

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 consider Adimurthi-Druet type functionals on compact surfaces with conical singularities and discuss the existence of extremals for such functionals extending previous results by Castò and Roy.

38 pages

Cited by in corpus (4)

• Improved Adams-type inequalities and their extremals in dimension 2m
• On the equivalence between an Onofri-type inequality by Del Pino-Dolbeault and the sharp logarithmic Moser-Trudinger inequality
• Anisotropic Moser-Trudinger inequality involving $L^n$ norm
• Blow-up analysis concerning singular Trudinger-Moser inequalities in dimension two