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Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals


Authors: Gianni Dal Maso, Irene Fonseca and Giovanni Leoni
Journal: Trans. Amer. Math. Soc. 370 (2018), 2785-2823
MSC (2010): Primary 49J45
DOI: https://doi.org/10.1090/tran/7151
Published electronically: December 26, 2017
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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.


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Additional Information

Gianni Dal Maso
Affiliation: SISSA, Via Bonomea 265, 34136 Trieste, Italy

Irene Fonseca
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

Giovanni Leoni
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

DOI: https://doi.org/10.1090/tran/7151
Received by editor(s): August 30, 2016
Received by editor(s) in revised form: November 22, 2016
Published electronically: December 26, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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