Bellettini, Giovanni and Paolini, Maurizio:
Teoremi di confronto tra diverse nozioni di movimento secondo la curvatura media
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 6 (1995), fasc. n.1, p. 45-54, (Italian)
pdf (1.19 MB), djvu (245 Kb). | MR1340281 | Zbl 0834.35062
Sunto
In questa Nota presentiamo alcuni teoremi di confronto tra il movimento secondo la curvatura media ottenuto con il metodo delle minime barriere di De Giorgi e i movimenti definiti con i metodi di Evans-Spruck, Chen-Giga-Goto, Giga-Goto-Ishii-Sato.
Referenze Bibliografiche
[2] L. AMBROSIO - H.-M. SONER, A level set approach to the evolution of surfaces of any codimension. Preprint Scuola Normale Superiore di Pisa, Ottobre 1994.
[4]
G. BELLETTINI -
M. PAOLINI,
Two examples of fattening for the curvature flow with a driving force.
Rend. Mat. Acc. Lincei, s. 9, v.
5,
1994, 229-236. |
fulltext bdim |
MR 1298266 |
Zbl 0826.35051[5] G. BELLETTINI - M. PAOLINI, Some comparison results between different notions of motion by mean curvature. Rendiconti Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica, in corso di stampa.
[6]
K. A. BRAKKE,
The Motion of a Surface by its Mean Curvature.
Princeton University Press, Princeton
1978. |
MR 485012 |
Zbl 0386.53047[7]
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[8]
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[11]
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[12]
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[13]
E. DE GIORGI,
New problems on minimizing movements. In:
J.-L. LIONS -
C. BAIOCCHI (eds.),
Boundary Value Problems for Partial Differential Equations and Applications.
29 Masson, Paris
1993. |
MR 1260440 |
Zbl 0851.35052[14] E. DE GIORGI, Barriere, frontiere, e movimenti di varietà. Conferenza tenuta al Dipartimento di Matematica dell'Università di Pavia, 18 marzo 1994.
[15]
P. DE MOTTONI -
M. SCHATZMAN,
Geometrical evolution of developped interfaces.
Trans. Amer. Math. Soc., in corso di stampa. |
Zbl 0797.35077[16]
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[23]
Y. GIGA -
S. GOTO -
H. ISHII,
Global existence of weak solutions for interface equations coupled with diffusion equations.
SIAM J. Math. Anal.,
23,
1992, 821-835. |
fulltext (doi) |
MR 1166559 |
Zbl 0754.35061[24]
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[28]
T. ILMANEN,
The level-set flow on a manifold. In:
Proceedings of Symposia in Pure Mathematics.
Amer. Math. Soc.,
54, Part I,
1993, 193-204. |
MR 1216585 |
Zbl 0827.53014[31]
T. ILMANEN,
Elliptic Regularization and Partial Regularity for Motion by Mean Curvature.
Memoirs of the Amer. Math. Soc.,
250,
1994, 1-90. |
MR 1196160 |
Zbl 0798.35066[32]
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. |
fulltext (doi) |
MR 973743 |
Zbl 0645.35025[33]
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[34]
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[35]
L. MODICA -
S. MORTOLA,
Un esempio di \( \Gamma \)-convergenza.
Boll. Un. Mat. Ital., B (5),
14,
1977, 285-299. |
MR 445362 |
Zbl 0356.49008[36]
S. OSHER -
J. A. SETHIAN,
Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations.
J. Comput. Phys.,
79,
1988, 12-49. |
fulltext (doi) |
MR 965860 |
Zbl 0659.65132[38]
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[39]
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