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

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

2010-01-14

arxiv.org/abs/1001.2540v1

Nonlinear Analysis 75 (2012) 612-624

Mathematics

Functional Analysis

Scientific paper

10.1016/j.na.2011.08.063

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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