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arXiv · 1001.2540

Sharp Nash Inequalities on the unit sphere. The influence of symmetries

Athanase Cotsiolis·Nikos Labropoulos
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Abstract

In this paper both we establish the best constants for the Nash inequalities on the standard unit sphere $\mathbb{S}^n$ of $\mathbb{R}^{n+1}$ and we give answers on the existence of extremal functions on the corresponding problems. Also we study the problem of the best constants in the case, where the data are invariant under the action of the group $G=O(k)\times O(m)$, and we find the best constants.

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Athanase Cotsiolis, Nikos Labropoulos. 2010-01-14. Sharp Nash Inequalities on the unit sphere. The influence of symmetries. https://doi.org/10.1016/j.na.2011.08.063

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