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May  2017, 16(3): 973-998. doi: 10.3934/cpaa.2017047

## Equivalence of sharp Trudinger-Moser-Adams Inequalities

 Department of Mathematics, University of British Columbia, The Pacific Institute for the Mathematical Sciences, Vancouver, BC V6T1Z4, Canada

Received  October 2016 Revised  January 2017 Published  February 2017

Fund Project: Research of this work was partially supported by the PIMS-Math Distinguished Post-doctoral Fellowship from the Pacific Institute for the Mathematical Sciences.

Improved Trudinger-Moser-Adams type inequalities in the spirit of Lions were recently studied in [21]. The main purpose of this paper is to prove the equivalence of these versions of the Trudinger-Moser-Adams type inequalities and to set up the relations of these Trudinger-Moser-Adams best constants. Moreover, using these identities, we will investigate the existence and nonexistence of the optimizers for some Trudinger-Moser-Adams type ineq

Citation: Nguyen Lam. Equivalence of sharp Trudinger-Moser-Adams Inequalities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 973-998. doi: 10.3934/cpaa.2017047
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##### References:
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