Remainder terms in the fractional Sobolev inequality

By Shibing Chen, Rupert L. Frank, Tobias Weth. 2012

137 citations recorded by the source corpus.

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.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c3885b2265324be512564141bb3719da6a28be6d

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In Mechanics of Materials

Citations in the corpus

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