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.
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