Improved Adams-type inequalities and their extremals in dimension 2m

Abstract

In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^m(\Omega )$, where $\Omega$ is any bounded, smooth, open subset of ${\mathbb{R}}^{2m}$, $m\ge 1$. 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.

References in corpus (2)

• Extremal Functions for Singular Moser-Trudinger Embeddings
• Existence and Nonexistence of Extremals for critical Adams inequalities in R4 and Trudinger-Moser inequalities in R2

Cited by in corpus (2)

• Estimate for concentration level of the Adams functional and extremals for Adams-type inequality
• A sharp trace Adams' inequality in ${\mathbb{R}}^4$ and Existence of the extremals