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arXiv · 1205.5666

Remainder terms in the fractional Sobolev inequality

Shibing Chen·Rupert L. Frank·Tobias Weth
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Abstract

We show that the fractional Sobolev inequality for the embedding $\H \hookrightarrow L^{\frac{2N}{N-s}}(\R^N)$, $s \in (0,N)$ can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak $L^{\frac{N}{N-s}}$-norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fractional case where $s$ is an even integer.

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Shibing Chen, Rupert L. Frank, Tobias Weth. 2012-05-25. Remainder terms in the fractional Sobolev inequality. https://arxiv.org/abs/1205.5666

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