# On the boundary regularity of phase-fields for Willmore's energy

@article{Dondl2019OnTB,
title={On the boundary regularity of phase-fields for Willmore's energy},
author={P. Dondl and Stephan Wojtowytsch},
journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
year={2019},
volume={149},
pages={1017 - 1035}
}
• Published 2019
• Mathematics
• Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Abstract We demonstrate that Radon measures which arise as the limit of the Modica-Mortola measures associated with phase-fields with uniformly bounded diffuse area and Willmore energy may be singular at the boundary of a domain and discuss implications for practical applications. We furthermore give partial regularity results for the phase-fields uε at the boundary in terms of boundary conditions and counterexamples without boundary conditions.
1 Citations
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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 uniformExpand

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