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
Full-text PDF Free Access
References |
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Additional Information
J. P. Aubin and H. Frankowska, Set-Valued Functions, Birkhaüser, Boston, 1990
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)
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)
L. C. Evans and J. Spruck, Motion of level sets by mean curvature 1, J. Differential Geom. 33, 635–681 (1991)
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
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)
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)
M. E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Press, 1993
H. M. Soner, Motion of a set by the curvature of its boundary, J. Differential Equations 101, 313–372 (1993)
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
J. P. Aubin and H. Frankowska, Set-Valued Functions, Birkhaüser, Boston, 1990
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)
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)
L. C. Evans and J. Spruck, Motion of level sets by mean curvature 1, J. Differential Geom. 33, 635–681 (1991)
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
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)
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)
M. E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Press, 1993
H. M. Soner, Motion of a set by the curvature of its boundary, J. Differential Equations 101, 313–372 (1993)
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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Article copyright:
© Copyright 1996
American Mathematical Society
