# 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} }

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.

#### One Citation

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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 uniform… Expand

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