Publication 25-CNA-002

Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, I

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Leonard Kreutz
School of Computation, Information and Technology
Technical University of Münich
Garching bei München, 85748, Germany

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
giovanni@andrew.cmu.edu

Abstract: This paper addresses the asymptotic development of order 2 by the $\Gamma$-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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