Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals
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- by Gianni Dal Maso, Irene Fonseca and Giovanni Leoni PDF
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Abstract:
In this paper the study of a nonlocal second order Cahn–Hilliard-type singularly perturbed family of functions is undertaken. The kernels considered include those leading to Gagliardo fractional seminorms for gradients. Using $\Gamma$ convergence the integral representation of the limit energy is characterized leading to an anisotropic surface energy on interfaces separating different phases.References
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Additional Information
- Gianni Dal Maso
- Affiliation: SISSA, Via Bonomea 265, 34136 Trieste, Italy
- MR Author ID: 54170
- Irene Fonseca
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
- MR Author ID: 67965
- Giovanni Leoni
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
- MR Author ID: 321623
- Received by editor(s): August 30, 2016
- Received by editor(s) in revised form: November 22, 2016
- Published electronically: December 26, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 2785-2823
- MSC (2010): Primary 49J45
- DOI: https://doi.org/10.1090/tran/7151
- MathSciNet review: 3748585