Asymptotics for optimizers of the fractional Hardy–Sobolev inequality

Abstract

The existence of optimizers [Formula: see text] in the space [Formula: see text], with differentiability order [Formula: see text], for the Hardy–Sobolev inequality is established through concentration-compactness. The asymptotic behavior [Formula: see text] as [Formula: see text] and the summability information [Formula: see text] for all [Formula: see text] are then obtained. Such properties turn out to be optimal when [Formula: see text], in which case optimizers are explicitly known.