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@article{faucris.308579703,
abstract = {We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function u∈H˙^{s}(R^{N}) whose energy satisfies [Formula presented]SN,s^{[Formula presented]}≤‖u‖H˙^{s}(R^{N})≤[Formula presented]SN,s^{[Formula presented]}, where SN,s is the optimal Sobolev constant, the bound ‖u−U[z,λ]‖H˙^{s}(R^{N})≲‖(−Δ)^{s}u−u^{2s⁎−1}‖H˙^{−s}(R^{N}), holds for a suitable fractional Talenti bubble U[z,λ]. For functions u which are close to Talenti bubbles, we give the sharp asymptotic value of the implied constant in this inequality. As an application of this, we derive an explicit polynomial extinction rate for positive solutions to a fractional fast diffusion equation.},
author = {De Nitti, Nicola and König, Tobias},
doi = {10.1016/j.jfa.2023.110093},
faupublication = {yes},
journal = {Journal of Functional Analysis},
keywords = {Extinction profiles; Fractional fast diffusion equation; Fractional Sobolev inequality; Stability of critical points},
note = {CRIS-Team Scopus Importer:2023-08-04},
peerreviewed = {Yes},
title = {{Stability} with explicit constants of the critical points of the fractional {Sobolev} inequality and applications to fast diffusion},
volume = {285},
year = {2023}
}