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arXiv · 1706.02160

On the Boundary Regularity of Phase-Fields for Willmore's Energy

Patrick Dondl·Stephan Wojtowytsch
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Abstract

We demonstrate that Radon measures which arise as the limit of the Modica-Mortola measures associated to 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 $u_\epsilon$ at the boundary in terms of boundary conditions and counterexamples without boundary conditions.

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Patrick Dondl, Stephan Wojtowytsch. 2017-06-05. On the Boundary Regularity of Phase-Fields for Willmore's Energy. https://arxiv.org/abs/1706.02160

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