An inhomogeneous, anisotropic, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model

Abstract

We consider the sharp interface limit of a diffuse phase field model with prescribed
total mass taking into account a spatially inhomogeneous anisotropic interfacial energy and an
elastic energy. The main aim is the derivation of a weak formulation of an anisotropic, inhomogeneous,
elastically modified Gibbs–Thomson law in the sharp interface limit. To this end we
show that one can pass to the limit in the weak formulation of the Euler–Lagrange equation of
the diffuse phase field energy.