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arXiv · 2405.00941

Gagliardo-Nirenberg inequality with H\"older norms

Mengxia Dong
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Abstract

The classical Gagliardo-Nirenberg inequality, known as an interpolation inequality, involves Lebesgue norms of functions and their derivatives. We established an interpolation lemma to connect Lebesgue and H\"older spaces, thus extending the Gagliardo-Nirenberg inequality. This extension involved substituting arbitrary Sobolev norms with appropriate H\"older norms, allowing for a wider range of applicable parameters in the inequality.

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Mengxia Dong. 2024-05-02. Gagliardo-Nirenberg inequality with H\"older norms. https://arxiv.org/abs/2405.00941

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