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Stability theorems for Gagliardo–Nirenberg–Sobolev inequalities: a reduction principle to the radial case

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Abstract

In this paper we investigate the quantitative stability for Gagliardo–Nirenberg–Sobolev inequalities. The main result is a reduction theorem, which states that, to solve the problem of the stability for Gagliardo-Nirenberg-Sobolev inequalities, one can consider only the class of radial decreasing functions.

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Acknowledgments

The author wish to warmly thank F. Maggi for its enlightening advise during the development of this work, and L. Brasco, G. De Philippis and A. Pratelli for several useful discussions about the topic.

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  1. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 4, 56126 , Pisa, Italy

    B. Ruffini

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  1. B. Ruffini
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Correspondence to B. Ruffini.

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Ruffini, B. Stability theorems for Gagliardo–Nirenberg–Sobolev inequalities: a reduction principle to the radial case. Rev Mat Complut 27, 509–539 (2014). https://doi.org/10.1007/s13163-013-0144-0

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  • DOI: https://doi.org/10.1007/s13163-013-0144-0

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