A quantitative version of the sharp Sobolev inequality in the Sobolev space W^{1,p}(R^n), 1 < p < n, is established with a remainder term involving the distance from the family of extremals. This settles a classical problem posed by Brezis and Lieb in the eigthies.

The sharp Sobolev inequality in quantitative form / A.Cianchi; N.Fusco; F.Maggi; A.Pratelli. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 11:(2009), pp. 1105-1139. [10.4171/JEMS/176]

The sharp Sobolev inequality in quantitative form

CIANCHI, ANDREA;MAGGI, FRANCESCO;
2009

Abstract

A quantitative version of the sharp Sobolev inequality in the Sobolev space W^{1,p}(R^n), 1 < p < n, is established with a remainder term involving the distance from the family of extremals. This settles a classical problem posed by Brezis and Lieb in the eigthies.
11
1105
1139
A.Cianchi; N.Fusco; F.Maggi; A.Pratelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/362080
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