2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225617Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in "Analysis of the Willmore Functional" by T. Riviere (Invent. Math. 174), we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally square-integrable second fundamental form. We show that the limit immersion is smooth and that it satisfies the conformal Willmore equation: it is a critical point of the Willmore functional restricted to infinitesimal conformal variations.35 pagesDifferential GeometryAnalysis of PDEs53A05; 53C42; 58E15; 53A30; 35Jxxtext