Calculus of Variations and Geometric Measure Theory

B. Ruffini

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

created by ruffini on 22 Jun 2012
modified on 24 Mar 2021


Published Paper

Inserted: 22 jun 2012
Last Updated: 24 mar 2021

Journal: Rev. Mat. Complut.
Pages: 23
Year: 2012


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