Second-order Γ-limit for the Cahn–Hilliard functional with dirichlet boundary conditions, I

Irene Fonseca

doi:10.1007/s00526-025-03164-6

December 4, 2025Calculus of Variations and Partial Differential EquationsOpen Access

Second-order Γ-limit for the Cahn–Hilliard functional with dirichlet boundary conditions, I

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Key Points

Transition layer forms near domain boundary, indicating critical behavior in Cahn–Hilliard dynamics.
Analysis shows significant interface interactions based on Dirichlet boundary conditions and functional behavior.
Study explores asymptotic behavior of second-order Gamma-limit in the context of phase transitions.
Findings imply important implications for understanding interface phenomena in related mathematical models.

Implication

Analysis reveals transition layer near boundary for Cahn–Hilliard functional with Dirichlet conditions, highlighting interface dynamics.

Abstract

This paper addresses the asymptotic development of order 2 by the Γ 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.

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Cite This Study

Irene Fonseca (2025) studied this question.

synapsesocial.com/papers/693624984fa91c937236c0cd https://doi.org/10.1007/s00526-025-03164-6

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Second-order Γ-limit for the Cahn–Hilliard functional with dirichlet boundary conditions, I

Key Points

Implication

Abstract

Discussion

Cite This Study

Second-order Γ-limit for the Cahn–Hilliard functional with dirichlet boundary conditions, I

Key Points

Implication

Abstract

Discussion

Cite This Study

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