Uniqueness of motion by mean curvature perturbed by stochastic noise
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 1-23. 
@article{AIHPC_2004__21_1_1_0,
     author = {Souganidis, P. E. and Yip, N. K.},
     title = {Uniqueness of motion by mean curvature perturbed by stochastic noise},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1--23},
     publisher = {Elsevier},
     volume = {21},
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     zbl = {1057.35106},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2002.11.001/}
}
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Souganidis, P. E.; Yip, N. K. Uniqueness of motion by mean curvature perturbed by stochastic noise. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 1-23. doi : 10.1016/j.anihpc.2002.11.001. http://www.numdam.org/articles/10.1016/j.anihpc.2002.11.001/

[1] Ambrosio L., Geometric evolution problems, distance function and viscosity solutions, in: Ambrosio L., Dancer N. (Eds.), Calculus of Variations and Partial Differential Equations, Springer-Verlag, 1999. | MR | Zbl

[2] Angenent S.B., Some recent results on mean curvature flow, in: Recent Advances in Partial Differential Equations, RAM Res. Appl. Math., vol. 30, Masson, Paris, 1994. | MR | Zbl

[3] Angenent S.B., Ilmanen T., Chopp D.L., A computed example of nonuniqueness of mean curvature flow in R3, Comm. PDE 20 (1995) 1937-1958. | MR

[4] S.B. Angenent, T. Ilmanen, J.J.L. Velázquez, Fattening from smooth initial data in mean curvature flow, Preprint.

[5] Barles G., Soner H.M., Souganidis P.E., Front propagation and phase field theory, SIAM J. Control Optim. 31 (1993) 439-469. | MR | Zbl

[6] Barles G., Souganidis P.E., A new approach to front propagation problems: theory and applications, Arch. Rational Mech. Anal. 141 (1998) 237-296. | MR | Zbl

[7] Bellettini G., Paolini M., Two examples of fattening for the curvature flow with a driving force, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. 5 (1994) 229-236. | MR | Zbl

[8] Bertoin J., Lev́y Processes, Cambridge University Press, 1996.

[9] Brakke K., The Motion of a Surface by its Mean Curvature, Mathematical Notes, vol. 20, Princeton University Press, Princeton, NJ, 1978. | MR | Zbl

[10] Chen Y.G., Giga Y., Goto S., Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991) 749-786. | MR | Zbl

[11] Dirr N., Luckhaus S., Novaga M., A stochastic selection principle in case of fattening for curvature flow, Calc. Var. Partial Differential Equations 13 (2001) 405-425. | MR | Zbl

[12] Evans L.C., Spruck J., Motion of level sets by mean curvature. I, J. Differential Geom. 33 (1991) 635-681. | MR | Zbl

[13] Evans L.C., Soner H.M., Souganidis P.E., Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45 (1992) 1097-1123. | MR | Zbl

[14] T. Funaki, Singular limits of reaction diffusion equations and random interfaces, Preprint.

[15] Goto S., Generalized motion of noncompact hypersurfaces whose growth speed depends superlinearly on the curvature tensor, Differential Integral Equations 7 (1994) 323-343. | MR | Zbl

[16] Ilmanen T., Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature, J. Differential Geom. 38 (1993) 417-461. | MR | Zbl

[17] Ishii H., Souganidis P.E., Generalized motion of noncompact hypersurfaces with velocities having arbitrary growth on the curvature tensor, Tôhuko Math. J. 47 (1995) 227-250. | MR | Zbl

[18] Koo Y., A fattening principle for fronts propagating by mean curvature plus a driving force, Comm. PDE 24 (1999) 1035-1053. | MR | Zbl

[19] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Springer-Verlag, 1991. | MR | Zbl

[20] Lions P.-L., Souganidis P.E., Fully nonlinear stochastic partial differential equations, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 1085-1092. | MR | Zbl

[21] Lions P.-L., Souganidis P.E., Fully nonlinear stochastic partial differential equations: non-smooth equations and applications, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998) 735-741. | MR | Zbl

[22] Lions P.-L., Souganidis P.E., Fully nonlinear stochastic partial differential equations with semilinear stochastic dependence, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 617-624. | MR | Zbl

[23] Lions P.-L., Souganidis P.E., Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 783-790. | MR | Zbl

[24] Soner H.M., Motion of set by the curvature of its boundary, J. Differential Equations 101 (1993) 313-372. | MR | Zbl

[25] Souganidis P.E., Front propagation: theory and applications, in: Viscosity Solutions and their Applications, Lecture Notes in Math., vol. 1660, Springer-Verlag, 1997. | MR | Zbl

[26] Taylor J., II-mean curvature and weighted mean curvature, Acta Metall. Meter. 40 (1992) 1475-1485.

[27] Taylor J., Cahn J.W., Handwerker C.A., I-geometric models of crystal growth, Acta Metall. Meter. 40 (1992) 1443-1474.

[28] Yip N.K., Stochastic motion by mean curvature, Arch. Rational Mech. Anal. 144 (1998) 313-355. | MR | Zbl

[29] Yip N.K., Existence of dendritic crystal growth with stochastic perturbations, J. Nonlinear Sci. 8 (1998) 491-579. | MR | Zbl

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