A new diffuse-interface approximation of the Willmore flow

Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond intended sharp interface evolution. Here we introduce a new two-variable approximation includes rather simple but efficient penalization deviation from quasi-one dimensional structure fields. We justify property by Gamma convergence result for energies and matched asymptotic expansion flow. Ground states energy are shown be one-dimensional, contrast presence saddle solutions usual approximation. Finally present numerical simulations illustrate apply our approach problems where leads an undesired behavior.