A comparison theorem for crystalline evolution in the plane

Authors:
Yoshikazu Giga and Morton E. Gurtin

Journal:
Quart. Appl. Math. **54** (1996), 727-737

MSC:
Primary 80A22; Secondary 35Q99

DOI:
https://doi.org/10.1090/qam/1417236

MathSciNet review:
MR1417236

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**[AF]**J. P. Aubin and H. Frankowska,*Set-Valued Functions*, Birkhaüser, Boston, 1990**[AG]**S. Angenent and M. E. Gurtin,*Multiphase thermomechanics with interfacial structure*. 2.*Evolution of an isothermal interface*, Arch. Rational Mech. Anal.**108**, 323-391 (1989)**[CGG]**Y.-G. Chen, Y. Giga, and S. Goto,*Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations*, J. Differential Geom.**33**, 749-786 (1991)**[ES]**L. C. Evans and J. Spruck,*Motion of level sets by mean curvature*1, J. Differential Geom.**33**, 635-681 (1991)**[FG]**T. Fukui and Y. Giga,*Motion of a graph by nonsmooth weighted curvature*, Proceedings of the First World Congress of Nonlinear Analysts (ed. V. Lakshmikantham), Tampa, vol. 1, Walter de Gruyter, Berlin, 1996, pp. 47-56**[Gi]**P. M. Girão,*Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature*, SIAM J. Numer. Anal.**32**, 886-899 (1995)**[GK]**P. M. Girão and R. V. Kohn,*Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature*, Numer. Math.**67**, 41-70 (1994)**[Gu]**M. E. Gurtin,*Thermomechanics of Evolving Phase Boundaries in the Plane*, Oxford Press, 1993**[So]**H. M. Soner,*Motion of a set by the curvature of its boundary*, J. Differential Equations**101**, 313-372 (1993)**[Ta]**J. E. Taylor,*Constructions and conjectures in crystalline nondifferential geometry*, Monographs in Pure and Applied Mathematics, vol. 55 (ed. B. Lawson and K. Tanenblat), Pitman, London, 1991, pp. 321-336

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Additional Information

DOI:
https://doi.org/10.1090/qam/1417236

Article copyright:
© Copyright 1996
American Mathematical Society