JournalsjemsVol. 11 , No. 5DOI 10.4171/jems/176

The sharp Sobolev inequality in quantitative form

  • Andrea Cianchi

    Universita di Firenze, Italy
  • Nicola Fusco

    Università degli Studi di Napoli Federico II, Italy
  • Francesco Maggi

    The University of Texas at Austin, United States
  • Aldo Pratelli

    Universität Erlangen-Nürnberg, Germany
The sharp Sobolev inequality in quantitative form cover

Abstract

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.