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Asymptotic Estimates for Gagliardo–Nirenberg Embedding Constants

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Abstract

Sharp asymptotic information is determined for the Gagliardo–Nirenberg embedding constants in high dimension. This analysis is motivated by the earlier observation that the logarithmic Sobolev inequality controls the Nash inequality. Moreover, one sees here that Hardy's inequality can be interpreted as the asymptotic limit of the logarithmic Sobolev inequality.

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  1. Department of Mathematics, The University of Texas at Austin, Austin, TX, 78712-1082, USA

    William Beckner

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  1. William Beckner
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Beckner, W. Asymptotic Estimates for Gagliardo–Nirenberg Embedding Constants. Potential Analysis 17, 253–266 (2002). https://doi.org/10.1023/A:1016195512677

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