Comparison results between minimal barriers and viscosity solutions for geometric evolutions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, p. 97-131 
@article{ASNSP_1998_4_26_1_97_0,
     author = {Bellettini, Giovanni and Novaga, Matteo},
     title = {Comparison results between minimal barriers and viscosity solutions for geometric evolutions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {1},
     year = {1998},
     pages = {97-131},
     zbl = {0904.35041},
     mrnumber = {1632984},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_1_97_0}
}

Bellettini, Giovanni; Novaga, Matteo. Comparison results between minimal barriers and viscosity solutions for geometric evolutions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, pp. 97-131. http://www.numdam.org/item/ASNSP_1998_4_26_1_97_0/

[1] L. Ambrosio - H.-M. Soner, A level set approach to the evolution of surfaces of any codimension, J. Differential Geom. 43 (1996), 693-737. | MR 1412682 | Zbl 0868.35046

[2] B. Andrews, Contraction of convex hypersurfaces in Euclidean space, Calc. Var. Partial Differential Equations 2 (1994), 151-171. | MR 1385524 | Zbl 0805.35048

[3] B. Andrews, Contraction of convex hypersurfaces in Riemannian spaces, J. Differential Geom. 34 (1994), 407-431. | MR 1267897 | Zbl 0797.53044

[4] G. Barles - H.-M. Soner - P.E. Souganidis, Front propagation and phase field theory, SIAM J. Control Optim. 31 (1993), 439-469. | MR 1205984 | Zbl 0785.35049

[5] G. Bellettini, Alcuni risultati sulle minime barriere per movimenti geometrici di insiemi, Boll. Un. Mat. Ital. 11 (1997), 485-512. | Zbl 0893.35043

[6] G. Bellettini - M. Novaga, Minimal barriers for geometric evolutions, J. Differential Equations 139 (1997), 76-103. | MR 1467354 | Zbl 0882.35028

[7] G. Bellettini - M. Paolini, Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 19 (1995), 43-67. | MR 1387549 | Zbl 0944.53039

[8] G. Bellettini - M. Paolini, Anisotropic motion by mean curvature in the context of Finsler geometry, Hokkaido Math. J. 25 (1996), 537-566. | MR 1416006 | Zbl 0873.53011

[9] Y.G. Chen - Y. Giga - S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equation, J. Differential Geom. 33 (1991), 749-786. | MR 1100211 | Zbl 0696.35087

[10] M.G. Crandall - H. Ishii - P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1-67. | MR 1118699 | Zbl 0755.35015

[11] M.G. Crandall - P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 227 (1983), 1-42. | MR 690039 | Zbl 0599.35024

[12] E. De Giorgi, Barriers, boundaries, motion of manifolds, Conference held at Dipartimento di Matematica of Pavia, March 18, 1994.

[13] L.C. Evans - J. Spruck, Motion of level sets by mean curvature I, J. Differential Geom. 33 (1991), 635-681. | MR 1100206 | Zbl 0726.53029

[14] L.C. Evans - J. Spruck, Motion of level sets by mean curvature II, Trans. Amer. Math. Soc. 330 (1992), 321-332. | MR 1068927 | Zbl 0776.53005

[15] Y. Giga - S. Goto, Geometric evolution of phase-boundaries, On the evolution of phase boundaries (M.E. Gurtin and G.B. MacFadden, eds.) vol. IMAVMA43, Springer-Verlag, New York, 1992, 51-65. | MR 1226914 | Zbl 0771.35027

[16] Y. Giga - S. Goto - H. Ishii - M.H. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains, Indiana Univ. Math. J. 40 (1991), 443-470. | MR 1119185 | Zbl 0836.35009

[17] S. Goto, Generalized motion of hypersurfaces whose growth speed depends superlinearly on the curvature tensor, Differential Integral Equations 7 (1994), 323-343. | MR 1255892 | Zbl 0808.35007

[18] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), 237-266. | MR 772132 | Zbl 0556.53001

[19] G. Huisken - T. Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality, in preparation.

[20] T. Ilmanen, The level-set flow on a manifold, Proc. Symp. Pure Math. 54 (1993), 193-204. | MR 1216585 | Zbl 0827.53014

[21] T. Ilmanen, Generalized flow of sets by mean curvature on a manifold, Indiana Univ. Math. J. 41 (1992), 671-705. | MR 1189906 | Zbl 0759.53035

[22] H. Ishii - P.E. Souganidis, Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor, Tohoku Math. J. 47 (1995), 227-250. | MR 1329522 | Zbl 0837.35066

[23] P.-L. Lions, "Generalized solutions of Hamilton-Jacobi equations", Pitman Research Notes in Mathematics, Boston, 1982. | MR 667669 | Zbl 0497.35001

[24] A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems", Birkhäuser, Boston, 1995. | MR 1329547 | Zbl 0816.35001

[25] H.-M. Soner, Motion of a set by the curvature of its boundary, J. Differential Equations 101 (1993), 313-372. | MR 1204331 | Zbl 0769.35070