Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, I

Irene Fonseca; Leonard Kreutz; Giovanni Leoni

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arXiv · 2501.10452

Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, I

Irene Fonseca·Leonard Kreutz·Giovanni Leoni

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Abstract

This paper addresses the asymptotic development of order 2 by the $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions. The Dirichlet data are assumed to be well separated from one of the two wells. In the case where there are no interfaces, it is shown that there is a transition layer near the boundary of the domain.

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Irene Fonseca, Leonard Kreutz, Giovanni Leoni. 2025-01-14. Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, I. https://arxiv.org/abs/2501.10452

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