The best constant of the Moser-Trudinger inequality on 𝑆²

Sano, Yuji

doi:10.1090/S0002-9947-03-03483-4

The best constant of the Moser-Trudinger inequality on $\textbf {S}^2$
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by Yuji Sano

Trans. Amer. Math. Soc. 356 (2004), 3477-3482

DOI: https://doi.org/10.1090/S0002-9947-03-03483-4

Published electronically: November 25, 2003

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Abstract:

We consider the best constant of the Moser-Trudinger inequality on $\textbf {S}^2$ under a certain orthogonality condition. Applying Moser’s calculation, we construct a counterexample to the sharper inequality with the condition.

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