Uniform regularity and convergence of phase-fields for Willmore’s energy

@article{Dondl2015UniformRA,
  title={Uniform regularity and convergence of phase-fields for Willmore’s energy},
  author={P. Dondl and Stephan Wojtowytsch},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2015},
  volume={56},
  pages={1-22}
}
We investigate the convergence of phase fields for the Willmore problem away from the support of a limiting measure $$\mu $$μ. For this purpose, we introduce a suitable notion of essentially uniform convergence. This mode of convergence is a natural generalisation of uniform convergence that precisely describes the convergence of phase fields in three dimensions. More in detail, we show that, in three space dimensions, points close to which the phase fields stay bounded away from a pure phase… Expand

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Phase-field approximations of the Willmore functional and flow
On the boundary regularity of phase-fields for Willmore's energy
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