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<p>This paper addresses the asymptotic development of order 2 by the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation> -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.</p>

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Second-order \(\Gamma \)-limit for the Cahn–Hilliard functional with dirichlet boundary conditions, I

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  • 发表日期：

    2025年12月4日

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  • Irene Fonseca,
  • Leonard Kreutz,
  • Giovanni Leoni

摘要

This paper addresses the asymptotic development of order 2 by the \(\Gamma \) Γ -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.