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

2017/06/05 by Dondl, Patrick, Wojtowytsch, Stephan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.02160

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_ε at the boundary in terms of boundary conditions and counterexamples without boundary conditions.

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