The Compactness of Extremals for a Singular Hardy-Trudinger-Moser Inequality (Journal of Partial Differential Equations, 2024)
Motivated by a recent work of Wang-Yang [19] , we study the compactnessof extremals $\{u_β\}$ for singular Hardy-Trudinger-Moser inequalities due to Hou [24] . Inparticular, 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.