Weak solutions of the curve shortening flow

Calculus of Variations and Partial Differential Equations

Volumn 5, Issue 6, 1997, Pages 489-510

  Deckelnick, Klaus ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142537449     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050076     Document Type: Article

References (14)

1. Altschuler, S.: Singularities of the curve shortening flow for space curves, J. Differential Geometry 34, 491-514 (1991)
2. Altschuler, S.: Grayson, M: Shortening space curves and flow through singularities, J. Differential Geometry 35, 283-295 (1992)
3. Ambrosio, L., Soner, H.M.: Level set approach to mean curvature flow in arbitrary codimension, Preprint (1994)
4. Angenent, S.: Parabolic equations for curves on surfaces Part I. Curves with p-integrable curvature, Annals of Mathematics, 132, 451-483 (1990). Part II. Intersection, blow-up and generalized solutions, Annals of Mathematics, 133, 171-215 (1991)
5. Angenent, S.: Parabolic equations for curves on surfaces Part I. Curves with p-integrable curvature, Annals of Mathematics, 132, 451-483 (1990). Part II. Intersection, blow-up and generalized solutions, Annals of Mathematics, 133, 171-215 (1991)
6. Brakke, K.A.: The motion of a surface by its mean curvature. Math. Notes, Princeton University Press, Princeton, NJ, 1978
7. Buttazzo, G.: Semicontinuity, relaxation and integral representation in the calculus of variations. Pitman Res. Notes in Math. 207, 1989
8. Deckelnick, K.: Schwache Lösungen für den Krümmungsfluß von Kurven, Habilitationsschrift, Freiburg (1995)
9. Gage, M., Hamilton, R.S.: The heat equation shrinking convex plane curves, J. Differential Geometry 23, 69-96 (1986)
10. Grayson, M.: The heat equation shrinks embedded plane curves to round points, J. Differential Geometry 26, 285-314 (1987)
11. Ilmanen, T.: Elliptic Regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. No. 1304 (1993)
12. Ioffe, A.D.: On lower Semicontinuity of integral functional I, II, SIAM J. Cont. Optim. 15, 521-538 and 991-1000 (1977)
13. Ladyzhenskaya, O.A., Solonnikov, V.A., Uraltseva, N.N.: Linear and quasilinear equations of parabolic type, Transl., II .Ser., Am. Math. Soc. 23 1968
14. Temam, R.: Navier Stokes Equations, North-Holland Pub. Co., Amsterdam New York Tokyo 1977