A fattening principle for fronts propagating by mean curvature plus a driving force

Communications in Partial Differential Equations

Volumn 24, Issue 5-6, 1999, Pages 1035-1053

  Koo, Yonghoi ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475120     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309908821457     Document Type: Article

References (19)

1. S. Angenent, On the formation of singularities in the curve shortening flow J. Diff. Geom. 33 (1991), 601-633.
2. 3, Comm. Partial Diff. Eq. 20 (1995), 1937-1958.
3. G. Barles and C. Georgelin, A simple proof of convergence for an approximation scheme for computing motion by mean curvature, SIAM J. Num. Anal. 32 (1995), 484-500.
4. G. Barles, H. M. Soner, and P. E. Souganidis, Front propagation and phase field theory, SIAM J. Cont. Optim. 31 (1993), 439-469.
5. G. Belletini and M. Paolini, Two examples of fattening for the mean curvature flow with a driving force, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. 9 Mat. Appl. 5 (1994), 229-236.
6. K. A. Brakke The motion of a surface by its mean curvature, Princeton University Press, NJ, 1978.
7. Y. G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. of Diff. Geom. 33 (1991), 749-786.
8. B. Chow and R. Gulliver, Aleksandrov reflection and geometric evolution of hypersurfaces, preprint.
9. M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-43.
10. M. G. Crandall, L. C. Evans, and P. L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487-502.
11. M. G. Crandall, H. Ishii, and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67.
12. L. C. Evans and J. Spruck, Motions of level sets by mean curvature I, J. Diff. Geom. 33 (1991), 635-681.
13. Y. Giga, S. Goto, H. Ishii and M. H. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains, Indiana Univ. Math. 40 (1991), 443-470.
14. H. Ishii and P. Souganidis Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor, Tohoku Math. J. 47 (1995), 227-250.
15. H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's, Comm. Pure Appl. Math. 42 (1989), 15-45.
16. R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational. Mech. Anal. 101 (1988), 1-27.
17. P. L. Lions, Optimal control of diffusion processes and Hamiton-Jacobi-Bellman equations. I Comm. Partial Diff. Eq. 8 (1983), 1101-1134.
18. S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comp. Phys. 79 (1988), 12-49.
19. M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice Hall, 1967.