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 text pdf 10.1512/iumj.2013.62.5065 10.1512/iumj.2013.62.5065 en Indiana Univ. Math. J. 62 (2013) 1381 - 1397 state-of-the-art mathematics http://iumj.org/access/