Sharp interface limit of a multi-phase transitions model under nonisothermal conditions
Riccardo Cristoferi, Giovanni Gravina · Calculus of Variations and Partial Differential Equations · 2021
Abstract A vectorial Modica–Mortola functional is considered and the convergence to a sharp interface model is studied. The novelty of the paper is that the wells of the potential are not constant, but depend on the spatial position in the domain $$\Omega $$ Ω . The mass constrained minimization problem and the case of Dirichlet boundary conditions are also treated. The proofs rely on the precise understanding of minimizing geodesics for the degenerate metric induced by the potential.