The sharp Sobolev inequality in quantitative form

Andrea Cianchi; Nicola Fusco; Francesco Maggi; Aldo Pratelli

doi:10.4171/jems/176

JournalsjemsVol. 11, No. 5pp. 1105–1139

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

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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.

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. 1105–1139

DOI 10.4171/JEMS/176