A quantitative version of the sharp Sobolev inequality in W_1,p (ℝ_n), 1 < p < n, is established with a remainder term involving the distance from the family of extremals.
Cite this article
Andrea Cianchi, Nicola Fusco, Francesco Maggi, Aldo Pratelli, The sharp Sobolev inequality in quantitative form. J. Eur. Math. Soc. 11 (2009), no. 5, pp. 1105–1139DOI 10.4171/JEMS/176