Inserted: 22 jun 2012
Last Updated: 10 dec 2013
Journal: Revista Matemática Complutense
A symmetrization techique, introduced by Cianchi, Fusco, Maggi and Pratelli concerning the Sobolev inequality, in "The sharp Sobolev inequality in quantitative form" (JEMS) , 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.
Keywords: Sobolev inequality, Gagliardo Nirenberg inequalities, stability inequalities