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arXiv · 1601.08127

On the rate of change of the best constant in the Sobolev inequality

Tom Carroll·Mouhamed Moustapha Fall·Jesse Ratzkin
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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.

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Tom Carroll, Mouhamed Moustapha Fall, Jesse Ratzkin. 2016-01-29. On the rate of change of the best constant in the Sobolev inequality. https://doi.org/10.1002/mana.201600277

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