Calculus of Variations and Geometric Measure Theory

R. Cristoferi - G. Gravina

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

created by cristoferi on 19 Jan 2020
modified on 14 Sep 2021


Published Paper

Inserted: 19 jan 2020
Last Updated: 14 sep 2021

Journal: Calc. Var. Partial Differential Equations
Volume: 60
Number: 142
Year: 2021

ArXiv: 2001.06852 PDF
Links: Published Paper


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.