期刊
ADVANCES IN CALCULUS OF VARIATIONS
卷 4, 期 1, 页码 1-81出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/ACV.2010.022
关键词
Dirichlet boundary conditions; Willmore surfaces of revolution
资金
- Deutsche Forschungsgemeinschaft [DE 611/5.1]
We consider the Willmore boundary value problem for surfaces of revolution where, as Dirichlet boundary conditions, any symmetric set of position and angle may be prescribed. Using direct methods of the calculus of variations, we prove existence and regularity of minimising solutions. Moreover, we estimate the optimal Willmore energy and prove a number of qualitative properties of these solutions. Besides convexity-related properties we study in particular the limit when the radii of the boundary circles converge to 0, while the length of the surfaces of revolution is kept fixed. This singular limit is shown to be the sphere, irrespective of the prescribed boundary angles. These analytical investigations are complemented by presenting a numerical algorithm, based on C-1-elements, and numerical studies. They intensively interact with geometric constructions in finding suitable minimising sequences for the Willmore functional.
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