(untitled) (Journal of Partial Differential Equations, 2024)
Motivated by a recent work of Wang-Yang [19] , we study the compactness of extremals {u_β} for singular Hardy-Trudinger-Moser inequalities due to Hou [24] . In particular, by the method of blow-up analysis, we conclude that, up to a subsequence, u_β converges to an extremal in some sense as β tends to zero.