The diffuse interface approximation of the Willmore functional in configurations with interacting phase boundaries

Abstract

In this thesis we study a diffuse interface approximation of the sum of the area and Willmore functional for which Gamma-convergence has already been established in the case of small space dimensions and smoothly bounded sets. We extend this result to a larger class of configurations with nonsmooth phase boundaries and explicitly allow intersecting boundary curves. We also analyze the interaction of parallel planar phase phields and discuss their slow motion under the L2-gradient flow of the diffuse Willmore functional. Moreover, we prove the existence of a new class of periodic entire solutions to the stationary Allen-Cahn equation in two dimensions.