Phase field models for thin elastic structures with topological constraint

created by lemenant on 11 Jul 2015
modified by wojtowytsch on 28 Oct 2016

[BibTeX]

Accepted Paper

Inserted: 11 jul 2015
Last Updated: 28 oct 2016

Journal: Arch Rational Mech Anal
Year: 2016
Doi: 10.1007/s00205-016-1043-6
We prove that in two dimensions, sequences of phase fields with uniformly bounded diffuse Willmore energy and diffuse area converge uniformly to the zeros of a double-well potential away from the support of a limiting measure. In three dimensions, we show that they converge $\mathcal H^1$-almost everywhere on curves. This enables us to show $\Gamma$-convergence to a sharp interface problem that only allows for connected structures. The results also imply Hausdorff convergence of the level sets in two dimensions and a similar result in three dimensions.