Extremal functions for Trudinger–Moser inequalities with nonnegative weights

Using blow-up analysis, the author proves the existence of extremal functions for Trudinger–Moser inequalities with nonnegative weights on bounded Euclidean domains or compact Riemannian surfaces. This extends recent results of Yang (J. Differ. Equ. 258:3161–3193, 2015 ) and Yang–Zhu (Proc. Am. Math...

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Veröffentlicht in:	Journal of inequalities and applications 2018, Vol.2018 (1), p.125-15, Article 125
1. Verfasser:	Hou, Songbo
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Applications of Mathematics Blow-up analysis Extremal function Inequalities Mathematics Mathematics and Statistics Riemann surfaces Trudinger–Moser inequality
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Beschreibung
Zusammenfassung:	Using blow-up analysis, the author proves the existence of extremal functions for Trudinger–Moser inequalities with nonnegative weights on bounded Euclidean domains or compact Riemannian surfaces. This extends recent results of Yang (J. Differ. Equ. 258:3161–3193, 2015 ) and Yang–Zhu (Proc. Am. Math. Soc. 145:3953–3959, 2017 ).
ISSN:	1025-5834 1029-242X 1029-242X
DOI:	10.1186/s13660-018-1718-7