Stochastic motion by mean curvature

Archive for Rational Mechanics and Analysis

Volumn 144, Issue 4, 1998, Pages 313-355

  Yip, Nung Kwan ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032281587     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050120     Document Type: Article

References (35)

1. ALLEN, S. M., & CAHN, J., A Microscopic Theory for Antiphase Boundary Motion and Its Application to Domain Coarsening, Acta Metallurgica, 27 (1979), 1085-1095.
2. ALMGREN, F., TAYLOR, J., & WANG, L., Curvature Driven Flows: A Variational Approach, SIAM J. Control Optim. 31 (1993). 387-438.
3. ALMGREN, F., & WANG, L., Mathematical Existence of Crystal Growth with Gibbs-Thomson Curvature Effects, (to appear in J. Geom. Anal.).
4. BILLINGSLEY, P., Convergence of Probability Measures, J. Wiley, 1968.
5. BRONSARD, L., & KOHN, R. V., Motion by mean curvature as the singular limit of Ginzburg-Landau model, J. Diff. Eqs. 90 (1991), 211-237.
6. BRAKKE, K. A., The motion of a surface by its mean curvature, Princeton University Press, 1978.
7. BARABÁSI, A. L., & STANLEY, H. E., Fractal Concepts in Surface Growth, Cambridge University Press, 1995.
8. CHEN, X., Generation and propagation of interfaces for reaction-diffusion equations, J. Diff. Eqs. 96 (1992), 116-141.
9. CHEN, Y. G., GIGA, Y., & GOTO, S., Uniqueness and Existence of Viscosity Solutions of Generalized Mean Curvature Flow Equations, J. Diff. Geom. 33 (1991), 749-786.
10. DAWSON, D. D., Measure-Valued Markov Processes, Ecole d'Eté de Probabilités de Saint-Flour XXI, ed. by P.L. HENNEQUIN, Lecture Notes in Mathematics, 1541, Springer-Verlag, 1991.
11. EVANS, L. C., & GARIEPY, R. F., Measure Theory and Fine Properties of Functions, CRC Press, 1992
12. EVANS, L. C., & SPRUCK, J., Motion of Level Sets by Mean Curvature. I, J. Diff. Geom. 33 (1991), 635-681.
13. FEDERER, H., Geometric Measure Theory, Springer-Verlag, 1969
14. FUNAKI, T., The scaling limit for a stochastic PDE and the separation of phases, Prob. Th. Related Fields 102 (1995), 221-288.
15. FUNAKI, T., Singular Limit for Stochastic Reaction-Diffusion Equation and Generation of Random Interfaces, preprint, Department of Mathematical Sciences, University of Tokyo, 1995.
16. GIUSTI, E., Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1994.
17. GURTIN, M. E., Thermomechanics of Evolving Phase Boundaries in the Plane, Clarendon Press, Oxford, 1993.
18. ILMANEN, T., Convergence of the Allen-Cahn Equation to Brakke's Motion by Mean Curvature, J. Diff. Geom. 38 (1993), 417-461.
19. JAKUBOWSKI, A., On Skorokhod Topology, Ann. Inst. Henri Poincaré 22 (1986), 263-285.
20. KESSLER, D. A., KOPLIK, J., & LEVINE, H., Pattern Selection in Fingered Growth Phenomena, Adv. Physics, 37 (1988), 255-339.
21. KRUG, J., & SPOHN, H., Kinetic roughening of growing surfaces in Solids Far From Equilibrium: Growth, Morphology and Defects; edited by C. GODRÈCHE, Cambridge University Press, 1991.
22. KARATZAS, I., & SHREVE, S. E., Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag, 1991.
23. KUNITA, H., Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990.
24. KAWASAKI, K. & OHTA, T., Kinetic Drumhead Models of Interface. I, Prog. Theor. Physics 67 (1982), 147-163.
25. KAWASAKI, K. & OHTA, T., Kinetic Drumhead Models of Interface. II, Prog. Theor. Physics 68 (1982), 129-147.
26. LANGER, J. S., Instabilities and Pattern Formation in Crystal Growth, Rev. Modern Physics 52 (1980), 1-28.
27. LUCKHAUS, S., Solutions for Two Phase Stefan Problem with the Gibbs-Thomson Law for the Melting Temperature, Euro. J. Appl. Math. 1 (1990), 101-111.
28. LUCKHAUS, S., & STURZENHECKER, T., Implicit Time Discretization for the Mean Curvature Flow Equation, Calc. Variations PDE, 3 (1995), 253-271.
29. DE MOTTONI, P., & SCHATZMAN, M., Geometric Evolution of Developed Interfaces, Trans. Amer. Math. Soc. 347 (1995), 1533-1589.
30. SONER, H. M., Ginzburg-Landau equation and motion by mean curvature, I: convergence, preprint, Carnegie Mellon University, 1992.
31. TAYLOR, J., CAHN, J. W., & HANDWERKER, C. A., Geometric Models of Crystal Growth, Acta Metall. Mater. 40 (1992), 1443-1474.
32. TAYLOR, J., Mean Curvature and Weighted Mean Curvature, Acta Metall. Mater. 40 (1992), 1475-1485.
33. STROOCK, D., & VARADHAN, S. R., Multidimensional Diffusion Processes, Springer-Verlag, 1979.
34. YIP, N. K., Stochastic Perturbations in Curvature Driven Flows, Thesis, Princeton University, 1996.
35. ZANGWILL, A., Theory of Growth-Induced Surface Roughness, preprint, 1995.