A phase-field approximation of the Willmore flow with volume and area constraints
Analysis of PDEs
2012-12-27 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1204.4274,
title = {A phase-field approximation of the Willmore flow with volume and area constraints},
author = {Pierluigi Colli and Philippe Laurencot},
journal= {arXiv preprint arXiv:1204.4274},
year = {2012}
}