On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form

Ishiwata, Michinori; Nakamura, Makoto; Wadade, Hidemitsu

doi:10.1016/j.anihpc.2013.03.004

Ishiwata, Michinori ; Nakamura, Makoto ; Wadade, Hidemitsu

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 297-314.

Résumé

In this article, we establish the weighted Trudinger–Moser inequality of the scaling invariant form including its best constant and prove the existence of a maximizer for the associated variational problem. The non-singular case was treated by Adachi and Tanaka (1999) [1] and the existence of a maximizer is a new result even for the non-singular case. We also discuss the relation between the best constants of the weighted Trudinger–Moser inequality and the Caffarelli–Kohn–Nirenberg inequality in the asymptotic sense.

MR Zbl

DOI : 10.1016/j.anihpc.2013.03.004

Classification : 46E35, 35J20
Mots clés : Weighted Trudinger–Moser inequality, Existence of maximizer, Caffarelli–Kohn–Nirenberg inequality with asymptotics

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     title = {On the sharp constant for the weighted {Trudinger{\textendash}Moser} type inequality of the scaling invariant form},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {297--314},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.03.004},
     mrnumber = {3181671},
     zbl = {1311.46034},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.004/}
}

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Ishiwata, Michinori; Nakamura, Makoto; Wadade, Hidemitsu. On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 2, pp. 297-314. doi : 10.1016/j.anihpc.2013.03.004. http://www.numdam.org/articles/10.1016/j.anihpc.2013.03.004/

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