University of Birmingham > Talks@bham > Analysis seminar > Bounds for the rate of change of the Sobolev constant

Bounds for the rate of change of the Sobolev constant

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The Sobolev constant of a bounded region in Euclidean space decreases as the region expands. Isoperimetric bounds for the rate of decrease of the Sobolev constant are obtained. These apply, in particular, to the first Dirichlet eigenfunction of the Laplacian and to the (inverse of the) torsional rigdity. The main ingredients are a fairly standard Hadamard variation formula and a reverse Holder inequality for the eigenfuntions. This is joint work with Jesse Ratzkin and Moustapha Fall.

This talk is part of the Analysis seminar series.

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