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Bellettini, Giovanni and Paolini, Maurizio:
Two examples of fattening for the curvature flow with a driving force (Due esempi di «rigonfiamento» per il moto secondo la curvatura con termine forzante)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 5 (1994), fasc. n.3, p. 229-236, (English)
pdf (955 Kb), djvu (225 Kb). | MR1298266 | Zbl 0826.35051

Sunto

Vengono dati due esempi di una curva regolare che evolve secondo la curvatura con un termine forzante, e dopo un certo tempo perde regolarità e degenera in un insieme con parte interna.
Referenze Bibliografiche
[1] F. ALMGREN - J. E. TAYLOR - L. WANG, Curvature-driven flows: a variational approach. SIAM J. Control Optim., 31, 1993, 387-437. | fulltext (doi) | MR 1205983 | Zbl 0783.35002
[2] S. ANGENENT, On the formation of singularities in the curve shortening flow. J. Differential Geom., 33, 3, 1991, 601-633. | fulltext mini-dml | MR 1100205 | Zbl 0731.53002
[3] G. BARLES - H. M. SONER - P. E. SOUGANIDIS, Front propagation and phase field theory. SIAM J. Control Optim., 31, 1993, 439-469. | fulltext (doi) | MR 1205984 | Zbl 0785.35049
[4] K. A. BRAKKE, The Motion of a Surface by its Mean Curvature. Princeton University Press, Princeton 1978. | MR 485012 | Zbl 0386.53047
[5] L. BRONSARD - R. V. KOHN, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics. J. Differential Equations, 90, 1991, 211-237. | fulltext (doi) | MR 1101239 | Zbl 0735.35072
[6] 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. | fulltext mini-dml | MR 1100211 | Zbl 0696.35087
[7] M. G. CRANDALL - H. ISHII - P. L. LIONS, Users guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.), 27, 1992, 1-67. | fulltext mini-dml | fulltext (doi) | MR 1118699 | Zbl 0755.35015
[8] M. G. CRANDALL - P. L. LIONS, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 227, 1983, 1-42. | fulltext (doi) | MR 690039 | Zbl 0599.35024
[9] E. DE GIORGI, Some conjectures on flow by mean curvature. In: M. L. BENEVENTO - T. BRUNO - C. SBORDONE (eds.), Methods of real analysis and partial differential equations. Liguori, Napoli 1990. | Zbl 0840.35042
[10] E. DE GIORGI, Conjectures on limits of some quasi linear parabolic equations and flow by mean curvature. Lecture delivered at the meeting on Partial Differential Equations and Related Topics in honour of L. Niremberg, Trento, September 3-7, 1990. | Zbl 0802.35063
[11] E. DE GIORGI, Congetture sui limiti delle soluzioni di alcune equazioni paraboliche quasi lineari. In: Nonlinear Analysis. A Tribute in Honour of G. Prodi. S.N.S. Quaderni, Pisa 1991, 173-187. | Zbl 0840.35012
[12] L. C. EVANS - H.-M. SONER - P. E. SOUGANIDIS, Phase transitions and generalized motion by mean curvature. Comm. Pure Appl. Math., 45, 1992, 1097-1123. | fulltext (doi) | MR 1177477 | Zbl 0801.35045
[13] L. C. EVANS - J. SPRUCK, Motion of level sets by mean curvature. I. J. Differential Geom., 33, 1991, 635-681. | fulltext mini-dml | 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. | fulltext (doi) | MR 1068927 | Zbl 0776.53005
[15] L. C. EVANS - J. SPRUCK, Motion of level sets by mean curvature. III. J. Geom. An., 2, 1992, 121-150. | fulltext (doi) | MR 1151756 | Zbl 0768.53003
[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. | fulltext (doi) | MR 1119185 | Zbl 0836.35009
[17] M. GRAYSON, The heat equation shrinks embedded plane curves to round points. J. Differential Geom., 26, 1987, 285-314. | fulltext mini-dml | MR 906392 | Zbl 0667.53001
[18] G. HUISKEN, Asymptotic behavior for singularities of the mean curvature flow. J. Differential Geom., 31, 1990, 285-299. | fulltext mini-dml | MR 1030675 | Zbl 0694.53005
[19] T. ILMANEN, Generalized flow of sets by mean curvature on a manifold. Indiana Univ. Math. J., 41, 1992, 671-705. | fulltext (doi) | MR 1189906 | Zbl 0759.53035
[20] T. ILMANEN, Convergence of the Allen-Cahn equation to Brakkes motion by mean curvature. J. Differential Geom., 38, 1993, 417-461. | fulltext mini-dml | MR 1237490 | Zbl 0784.53035
[21] R. JENSEN, The maximum principle for viscosity solutions of second-order fully nonlinear partial differential equations. Arch. Rational Mech. Anal., 101, 1988, 1-27. | fulltext (doi) | MR 920674 | Zbl 0708.35019
[22] P.-L. LIONS, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, I. Comm. Partial Differential Equations, 8, 1983, 1101-1134. | fulltext (doi) | MR 709164 | Zbl 0716.49022
[23] M. PAOLINI - C. VERDI, Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter. Asymptotic Anal., 5, 1992, 553-574. | MR 1169358 | Zbl 0757.65078
[24] H. M. SONER, Motion of a set by the curvature of its boundary. J. Differential Equations, 101, 1993, 313-372. | fulltext (doi) | MR 1204331 | Zbl 0769.35070
[25] H. M. SONER, Ginzburg-Landau equation and motion by mean curvature, I: convergence. Research report n. 93-NA-026, August 1993, Carnegie Mellon University. | Zbl 0935.35060
[26] H.-M. SONER - P. E. SOUGANIDIS, Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature. Comm. Partial Differential Equations, 18, 1993, 859-894. | fulltext (doi) | MR 1218522 | Zbl 0804.53006

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