Calculus of Variations and Geometric Measure Theory
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P. Dondl - S. Wojtowytsch

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

created by wojtowytsch on 13 Sep 2018

[BibTeX]

preprint

Inserted: 13 sep 2018

Year: 2017

ArXiv: 1706.02160 PDF

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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