Date of Original Version

6-17-2014

Type

Article

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-015-0819-0

Abstract or Description

The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter ε that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to |s−1| β near s = 1, with 1 < β < 2. The first order term in the asymptotic development by Γ-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values

DOI

10.1007/s00526-015-0819-0

Included in

Mathematics Commons

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Published In

Calculus of Variations and Partial Differential Equations, 54, 1, 1119-1145.