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Applications of p-harmonic transplantation for functional inequalities involving a Finsler norm

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Abstract

In this paper, we prove several inequalities such as Sobolev, Poincaré, logarithmic Sobolev, which involve a general norm with accurate information of extremals, and are valid for some symmetric functions. We use Ioku’s transformation, which is a special case of p-harmonic transplantation, between symmetric functions.

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Acknowledgements

The authors thank Prof. Megumi Sano and Prof. Norisuke Ioku for fruitful discussions and giving us comments on this topic. This work was partly supported by Osaka City University Advanced Mathematical Institute MEXT Joint Usage / Research Center on Mathematics and Theoretical Physics JPMXP0619217849. The second author (F.T.) was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B), JP19H01800, and JSPS Grant-in-Aid for Scientific Research (S), JP19H05597.

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Authors and Affiliations

  1. Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Sadaf Habibi & Futoshi Takahashi

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  1. Sadaf Habibi
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  2. Futoshi Takahashi
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All authors have taken part in this research equally and they read and approved the final manuscript.

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Correspondence to Futoshi Takahashi.

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The authors declare that they have no competing interests.

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This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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Habibi, S., Takahashi, F. Applications of p-harmonic transplantation for functional inequalities involving a Finsler norm. Partial Differ. Equ. Appl. 3, 32 (2022). https://doi.org/10.1007/s42985-022-00168-1

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