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.

中文翻译：

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非等温条件下多相转变模型的锐界面极限

考虑了矢量 Modica-Mortola 泛函，并研究了向锐界面模型的收敛性。该论文的新颖之处在于势阱不是常数，而是取决于域\(\Omega \) 中的空间位置。质量约束最小化问题和狄利克雷边界条件的情况也被处理。证明依赖于对最小化由电位引起的退化度量的测地线的精确理解。