On the boundary regularity of phase-fields for Willmore's energy
Patrick Dondl, Stephan Wojtowytsch · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2018
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-fieldsuεat the boundary in terms of boundary conditions and counterexamples without boundary conditions.