Communications in Analysis and Geometry
Volume 19 (2011)
Local Palais–Smale sequences for the Willmore functional
Pages: 563 – 599
Using the reformulation in divergence form of the Euler–Lagrange equation for the Willmore functional as it was developed in the second author's paper, 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.