On the rate of change of the best constant in the Sobolev inequality
arXiv:1601.08127 · doi:10.1002/mana.201600277
Abstract
We estimate the rate of change of the best constant in the Sobolev inequality of a Euclidean domain which moves outward. Along the way we prove an inequality which reverses the usual Holder inequality, which may be of independent interest.
17 pages