Calculus of Variations and Geometric Measure Theory

L. Kreutz - I. Fonseca - G. Leoni

Second-Order Γ-Limit for the Cahn–Hilliard Functional with Dirichlet Boundary Conditions, I

created by kreutz on 21 Jan 2025

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Inserted: 21 jan 2025
Last Updated: 21 jan 2025

Pages: 57
Year: 2025

Abstract:

This paper addresses the asymptotic development of order 2 by the 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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