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<p>This paper continues the study of the asymptotic development of order 2 by <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 initiated in [<CitationRef CitationID="CR8">8</CitationRef>]. While in the first paper, the Dirichlet data are assumed to be well separated from one of the two wells, here this is no longer the case. We show that, in the absence of internal interfaces, the energy concentrates in a transition layer near the domain boundary.</p>

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Second-Order \(\Gamma \)-Limit for the Cahn–Hilliard Functional with Dirichlet Boundary Conditions, II

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  • 出版模式：

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  • 发表日期：

    2026年7月18日

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  • Irene Fonseca,
  • Leonard Kreutz,
  • Giovanni Leoni

摘要

This paper continues the study of the asymptotic development of order 2 by \(\Gamma \) Γ -convergence of the Cahn–Hilliard functional with Dirichlet boundary conditions initiated in [8]. While in the first paper, the Dirichlet data are assumed to be well separated from one of the two wells, here this is no longer the case. We show that, in the absence of internal interfaces, the energy concentrates in a transition layer near the domain boundary.