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, II

created by kreutz on 21 Jan 2025
modified on 24 Jan 2025

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Submitted Paper

Inserted: 21 jan 2025
Last Updated: 24 jan 2025

Pages: 39
Year: 2025

Abstract:

This paper continues the study of the asymptotic development of order 2 by Γ-convergence of the Cahn–Hilliard functional with Dirichlet boundary conditions initiated in 7. 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. 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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