Geodesic
On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations
Yoshikazu Giga1 ; Takeshi Ohtsuka1 orcid ; Reiner Schätzle2
1University of Tokyo, Japan
2Universität Tübingen, Germany
Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 317-348

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DOI

The convergence of solutions of anisotropic Allen–Cahn equations is studied when the interface thickness parameter (denoted by ε) tends to zero. It is shown that the convergence to a level set solution of the corresponding anisotropic interface equations is uniform with respect to the derivatives of a surface energy density function. As an application the crystalline motion of interfaces is shown to be approximated by the anisotropic Allen–Cahn equations.
DOI : 10.4171/ifb/146
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Anisotropic Allen–Cahn equation, anisotropic mean curvature flow, viscosity solution, crystalline curvature flow

Yoshikazu Giga  1   ; Takeshi Ohtsuka  1   ; Reiner Schätzle  2

1 University of Tokyo, Japan
2 Universität Tübingen, Germany 
Yoshikazu Giga; Takeshi Ohtsuka; Reiner Schätzle. On a uniform approximation of motion by anisotropic curvature by the Allen–Cahn equations. Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 317-348. doi: 10.4171/ifb/146
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     author = {Yoshikazu Giga and Takeshi Ohtsuka and Reiner Sch\"atzle},
     title = {On a uniform approximation of motion by anisotropic curvature by the {Allen{\textendash}Cahn} equations},
     journal = {Interfaces and free boundaries},
     pages = {317--348},
     year = {2006},
     volume = {8},
     number = {3},
     doi = {10.4171/ifb/146},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/146/}
}
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