Optimal decay of extremals for the fractional Sobolev inequality

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We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.

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Getting Acquainted with the Fractional Laplacian (2017, background): “See also [14] for decay estimates of ground states of a nonlinear nonlocal problem.”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “In [6, 38], several estimates on these minimizers were obtained, and it was conjectured that the solutions are dilations and translations of the radial function U(x) = 1 (1 + |x|p ) N−sp p , x ∈ Rn ,”
Nonlocal problems with critical Hardy nonlinearity (2017, methodology): “In [4] the existence and properties of solutions for the minimization problem (2.”