Existence and non-existence of maximizers for the Moser–Trudinger type inequalities under inhomogeneous constraints

Norihisa Ikoma, Michinori Ishiwata, Hidemitsu Wadade

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Abstract

In this paper, we study the existence and non-existence of maximizers for the Moser–Trudinger type inequalities in (Formula presented.) of the form (Formula presented.)Here (Formula presented.) and (Formula presented.) where (Formula presented.) and (Formula presented.) denotes the surface area of the unit ball in (Formula presented.). We show the existence of the threshold (Formula presented.) such that (Formula presented.) is not attained if (Formula presented.) and is attained if (Formula presented.). We also provide the conditions on (a, b) in order that the inequality (Formula presented.) holds.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalMathematische Annalen
DOIs
Publication statusAccepted/In press - 2018 Jun 9

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Keywords

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ASJC Scopus subject areas

  • Mathematics(all)

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