Stability theorems for GNS inequalities: a reduction principle to the radial case

2014/03/13 by Berardo Ruffini, Ruffini, Berardo
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1403.3387

arxiv created 2014/03/13 · arxiv updated 2014/03/14

Abstract

A symmetrization techique, introduced by Cianchi, Fusco, Maggi and Pratelli concerning the Sobolev inequality, is adapted to the Gagliardo-Nirenberg-Sobolev inequality (GNS) to obtain a reduction step of the problem of showing its quantitative version. More precisely we prove a stability result for the GNS inequality under the hypothesis that it holds, in turn, in the smaller class of radial symmetric decreasing functions.

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