The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions

Marco Cicalese; Yuko Nagase; Giovanni Pisante

doi:10.1515/ACV.2010.014

The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions

Marco Cicalese
, Yuko Nagase
, Giovanni Pisante

Università degli Studi di Napoli Federico II
University of Campania “Luigi Vanvitelli”

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we prove the Gibbs-Thomson relation between the coarse grained chemical potential and the non homogeneous and anisotropic mean curvature of a phase interface within the gradient theory of phase transitions thus proving a generalization of a conjecture stated by Gurtin and proved by Luckhaus and Modica in the homogeneous and isotropic case.

Original language	English
Pages (from-to)	321-344
Number of pages	24
Journal	Advances in Calculus of Variations
Volume	3
Issue number	3
DOIs	https://doi.org/10.1515/ACV.2010.014
State	Published - Jul 2010
Externally published	Yes

Keywords

Anisotropic phase transition
Finsler metrics
Gibbs-Thomson relation for surface tension

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10.1515/ACV.2010.014

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title = "The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions",

abstract = "In this paper we prove the Gibbs-Thomson relation between the coarse grained chemical potential and the non homogeneous and anisotropic mean curvature of a phase interface within the gradient theory of phase transitions thus proving a generalization of a conjecture stated by Gurtin and proved by Luckhaus and Modica in the homogeneous and isotropic case.",

keywords = "Anisotropic phase transition, Finsler metrics, Gibbs-Thomson relation for surface tension",

author = "Marco Cicalese and Yuko Nagase and Giovanni Pisante",

note = "Funding Information: Acknowledgments. The authors wish to thank Yoshihiro Tonegawa and Giovanni Bellettini for interesting discussions on the subject of this paper. The work by Marco Cicalese was partially supported by the European Research Council under FP7, Advanced Grant n. 226234 {\textquotedblleft}Analytic Techniques for Geometric and Functional Inequalities{\textquotedblright}. The work by Yuko Nagase was supported by {\textquotedblleft}Progetto Mecenas, Universit{\`a} di Napoli Federico II and Compagnia di S. Paolo{\textquotedblright}.",

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doi = "10.1515/ACV.2010.014",

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T1 - The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions

AU - Cicalese, Marco

AU - Nagase, Yuko

AU - Pisante, Giovanni

N1 - Funding Information: Acknowledgments. The authors wish to thank Yoshihiro Tonegawa and Giovanni Bellettini for interesting discussions on the subject of this paper. The work by Marco Cicalese was partially supported by the European Research Council under FP7, Advanced Grant n. 226234 “Analytic Techniques for Geometric and Functional Inequalities”. The work by Yuko Nagase was supported by “Progetto Mecenas, Università di Napoli Federico II and Compagnia di S. Paolo”.

PY - 2010/7

Y1 - 2010/7

N2 - In this paper we prove the Gibbs-Thomson relation between the coarse grained chemical potential and the non homogeneous and anisotropic mean curvature of a phase interface within the gradient theory of phase transitions thus proving a generalization of a conjecture stated by Gurtin and proved by Luckhaus and Modica in the homogeneous and isotropic case.

AB - In this paper we prove the Gibbs-Thomson relation between the coarse grained chemical potential and the non homogeneous and anisotropic mean curvature of a phase interface within the gradient theory of phase transitions thus proving a generalization of a conjecture stated by Gurtin and proved by Luckhaus and Modica in the homogeneous and isotropic case.

KW - Anisotropic phase transition

KW - Finsler metrics

KW - Gibbs-Thomson relation for surface tension

UR - https://www.scopus.com/pages/publications/84858425610

U2 - 10.1515/ACV.2010.014

DO - 10.1515/ACV.2010.014

M3 - Article

AN - SCOPUS:84858425610

SN - 1864-8258

VL - 3

SP - 321

EP - 344

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

IS - 3

ER -

The Gibbs-Thomson relation for non homogeneous anisotropic phase transitions

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Keywords

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