Sharp Nash inequalities on manifolds with boundary in the presence of symmetries

Details Sharp Nash inequalities on manifolds with boundary in the presence of symmetries Sharp Nash inequalities on manifolds with boundary in the presence of symmetries

2009-12-18

arxiv.org/abs/0912.3562v3

Nonlinear Analysis 74 (2011) 161-170

Mathematics

Functional Analysis

Scientific paper

10.1016/j.na.2010.08.030

In this paper we establish the best constant $\widetilde A_{opt}(\bar{M})$ for the Trace Nash inequality on a $n-$dimensional compact Riemannian manifold in the presence of symmetries, which is an improvement over the classical case due to the symmetries which arise and reflect the geometry of manifold. This is particularly true when the data of the problem is invariant under the action of an arbitrary compact subgroup $G$ of the isometry group $Is(M,g)$, where all the orbits have infinite cardinal.

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