Remainder terms in the fractional Sobolev inequality
Shuxing ChenRupert FrankTobias Weth
46E3539B6226A3326D10Sobolev inequalitystabilityfractional Laplacian
We show that the fractional Sobolev inequality for the embedding $\mathring{H}^{s/2}(\mathbb{R}^N)\hookrightarrow L^{2N/(N-s)}(\mathbb{R}^N)$, $s \in (0,N)$ 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 $L^{N/(N-s)}$-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.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.5065
10.1512/iumj.2013.62.5065
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Indiana Univ. Math. J. 62 (2013) 1381 - 1397
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