On the rate of change of the best constant in the Sobolev inequality
  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. 
Tom Carroll, Mouhamed Moustapha Fall, and Jesse Ratzkin
math.AP math.DG