Sharp interface limit of a multi-phase transitions model under nonisothermal conditions

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.

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.

Keywords

• nonlocal anisotropic model
• phase-transitions
• gradient theory
• singular perturbations
• variational-problems
• local minimizers
• asymptotic development
• gamma-convergence
• potentials
• boundaries