A phase-field approximation of the Willmore flow with volume and area constraints

Details A phase-field approximation of the Willmore flow with volume and area constraints A phase-field approximation of the Willmore flow with volume and area constraints

2012-04-19

arxiv.org/abs/1204.4274v1

Mathematics

Analysis of PDEs

Scientific paper

The well-posedness of a phase-field approximation to the Willmore flow with area and volume constraints is established when the functional approximating the area has no critical point satisfying the two constraints. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by a variational minimization principle. The main difficulty stems from the nonlinearity of the area constraint.

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