In this paper, we prove the existence of an extremal function for the Adams-Moser-Trudinger inequality on bounded, smooth, open sets of dimension 2m, m ≥ 1. Moreover, we extend this result to improved versions of Adams' inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions.
Improved Adams-type inequalities and their extremals in dimension 2m
Mancini G.
2021-01-01
Abstract
In this paper, we prove the existence of an extremal function for the Adams-Moser-Trudinger inequality on bounded, smooth, open sets of dimension 2m, m ≥ 1. Moreover, we extend this result to improved versions of Adams' inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions.File in questo prodotto:
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