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Equivalence of sharp Trudinger-Moser-Adams Inequalities

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

    Mathematics Subject Classification: Primary: 35A23; Secondary: 26D15, 46E35, 46E30.


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