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Extremal Functions for Singular Moser-Trudinger Embeddings

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arxiv 1601.05666 v1 pith:45HWE32B submitted 2016-01-21 math.AP

Stefano Iula , Gabriele Mancini This is my paper · ORCID
classification math.AP
keywords functionalssingulartypemoser-trudingeradimurthi-druetcarleson-changcastcompact
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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 Cast\`o and Roy.

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  1. Extremal functions for a singular Hardy-Moser-Trudinger inequality

    math.FA 2019-08 conditional novelty 6.0 of 10

    For every singular weight |x|^{-2β} and every α below the first Hardy eigenvalue, the supremum of ∫_B e^{4π(1−β)u²}|x|^{-2β} dx over the improved Hardy unit ball is finite and attained.

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