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

Sadaf Habibi; Futoshi Takahashi

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arXiv · 2111.11666

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

Sadaf Habibi·Futoshi Takahashi

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Abstract

In this paper, we prove several inequalities such as Sobolev, Poincar\'e, 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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Sadaf Habibi, Futoshi Takahashi. 2021-11-23. Applications of $p$-harmonic transplantation for functional inequalities involving a Finsler norm. https://arxiv.org/abs/2111.11666

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