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arXiv · 1403.3387

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

Berardo Ruffini
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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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Berardo Ruffini. 2014-03-13. Stability theorems for GNS inequalities: a reduction principle to the radial case. https://arxiv.org/abs/1403.3387

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