Optimal interface error estimates for the mean curvature flow

R. H. Nochetto; M. Paolini; C. Verdi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 2, page 193-212
  • ISSN: 0391-173X

How to cite

top

Nochetto, R. H., Paolini, M., and Verdi, C.. "Optimal interface error estimates for the mean curvature flow." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.2 (1994): 193-212. <http://eudml.org/doc/84174>.

@article{Nochetto1994,
author = {Nochetto, R. H., Paolini, M., Verdi, C.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {double equal well potential; phase transitions; singularities; interface},
language = {eng},
number = {2},
pages = {193-212},
publisher = {Scuola normale superiore},
title = {Optimal interface error estimates for the mean curvature flow},
url = {http://eudml.org/doc/84174},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Nochetto, R. H.
AU - Paolini, M.
AU - Verdi, C.
TI - Optimal interface error estimates for the mean curvature flow
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 2
SP - 193
EP - 212
LA - eng
KW - double equal well potential; phase transitions; singularities; interface
UR - http://eudml.org/doc/84174
ER -

References

top
  1. [1] S.M. Allen - J.W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsing. Acta Metall.27 (1979), 1085-1095. 
  2. [2] G. Barles - H.M. Soner - P.E. Souganidis, Front propagations and phase field theory. SIAM J. Control Optim.31 (1993), 439-469. Zbl0785.35049MR1205984
  3. [3] L. Bronsard - R.V. Kohn, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics. J. Differential Equations90 (1991), 211-237. Zbl0735.35072MR1101239
  4. [4] X. Chen, Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations96 (1992), 116-141. Zbl0765.35024MR1153311
  5. [5] X. Chen - C.M. Elliott, Asymptotics for a parabolic double obstacle problem. IMA preprint, 922 (1992), 1-25. 
  6. [6] 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. Zbl0840.35012
  7. [7] P. De Mottoni - M. Schatzman, Évolution géométrique d'interfaces. C.R. Acad. Sci. Paris Sér. I Math. 309 (1989), 453-458. Zbl0698.35078MR1055457
  8. [8] P. De Mottoni - M. Schatzman, Geometrical evolution of developed interfaces. Trans. Amer. Math. Soc. (to appear). Zbl0840.35010MR1672406
  9. [9] 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. Zbl0801.35045MR1177477
  10. [10] L.C. Evans - J. Spruck, Motion of level sets by mean curvature I. J. Differential Geom.33 (1991), 635-681. Zbl0726.53029MR1100206
  11. [11] E. Giusti, Minimal Surfaces and Functions of Bounded variation, Birkhäuser, Boston, 1984. Zbl0545.49018MR775682
  12. [12] M. Grayson, The heat equation shrinks embedded plane curves to round points. J. Differential Geom.26 (1987), 285-314. Zbl0667.53001MR906392
  13. [13] T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature, J. Differential Geom.38 (1993), 417-461. Zbl0784.53035MR1237490
  14. [14] J.B. Keller - J. Rubinstein - P. Sternberg, Fast reaction, slow diffusion and curve shortening. SIAM J. Appl. Math.49 (1989), 116-133. Zbl0701.35012MR978829
  15. [15] 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. Zbl0757.65078MR1169358

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.