Equivalence of sharp Trudinger-Moser-Adams Inequalities

Nguyen Lam

doi:10.3934/cpaa.2017047

Article Contents

2017, Volume 16, Issue 3: 973-998. Doi: 10.3934/cpaa.2017047

This issue Previous Article Multiple positive standing wave solutions for schrödinger equations with oscillating state-dependent potentials Next Article Positive ground state solutions of a quadratically coupled schrödinger system

Equivalence of sharp Trudinger-Moser-Adams Inequalities

Nguyen Lam

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

Received: September 30, 2016

Revised: December 31, 2016

Published: January 2018

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

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

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