Correctors and error estimates in the homogenization of a Mullins–Sekerka problem

Adriana Garroni; Barbara Niethammer

Annales de l'I.H.P. Analyse non linéaire (2002)

  • Volume: 19, Issue: 4, page 371-393
  • ISSN: 0294-1449

How to cite

top

Garroni, Adriana, and Niethammer, Barbara. "Correctors and error estimates in the homogenization of a Mullins–Sekerka problem." Annales de l'I.H.P. Analyse non linéaire 19.4 (2002): 371-393. <http://eudml.org/doc/78549>.

@article{Garroni2002,
author = {Garroni, Adriana, Niethammer, Barbara},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Mullins-Sekerka free boundary problem; first-order phase transformation},
language = {eng},
number = {4},
pages = {371-393},
publisher = {Elsevier},
title = {Correctors and error estimates in the homogenization of a Mullins–Sekerka problem},
url = {http://eudml.org/doc/78549},
volume = {19},
year = {2002},
}

TY - JOUR
AU - Garroni, Adriana
AU - Niethammer, Barbara
TI - Correctors and error estimates in the homogenization of a Mullins–Sekerka problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 4
SP - 371
EP - 393
LA - eng
KW - Mullins-Sekerka free boundary problem; first-order phase transformation
UR - http://eudml.org/doc/78549
ER -

References

top
  1. [1] Alikakos N., Fusco G., The equations of Ostwald ripening for dilute systems, J. Stat. Phys.95 (5/6) (1999) 851-866. Zbl0952.76089MR1712440
  2. [2] Alikakos N., Fusco G., Ostwald ripening for dilute systems under quasistationary dynamics, Comm. Math. Phys., to appear. Zbl1082.82005MR1993380
  3. [3] Chen X., Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Diff. Geometry44 (1996) 262-311. Zbl0874.35045MR1425577
  4. [4] Chen X., Hong J., Yi F., Existence, uniqueness and regularity of classical solutions of the Mullins–Sekerka problem, Comm. Part. Diff. Eq.21 (1996) 1705-1727. Zbl0884.35177MR1421209
  5. [5] Cioranescu D., Murat F., A strange term coming from nowhere, in: Cherkaev A., Kohn R.V. (Eds.), Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, 1997, pp. 45-94. Zbl0912.35020MR1493040
  6. [6] Escher J., Simonett G., Classical solutions for the quasi-stationary Stefan problem with surface tension, in: Demuth M. (Ed.), Papers associated with the International Conference on Partial Differential Equations, Potsdam, Germany, June 29–July 2, 1996, Akademie-Verlag, 1996, pp. 98-104. Zbl0880.35140MR1456181
  7. [7] Grisvard P., Elliptic Problems in Nonsmoooth Domains, Pitman, Boston, 1985. Zbl0695.35060MR775683
  8. [8] Kacimi H., Murat F., Estimation de l'erreur dans des problemes de Dirichlet ou apparait un terme etrange, in: Partial Differential Equations and the Calculus of Variations. Essays in Honor of Ennio De Giorgi, Birkhäuser, 1989, pp. 661-696. Zbl0687.35007MR1034024
  9. [9] Langer J.S., An introduction to the kinetics of first order phase transitions, in: Godrẽche C. (Ed.), Solids Far from Equilibrium, Cambridge University Press, 1992, pp. 297-362. 
  10. [10] Lifshitz I.M., Slyozov V.V., The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids19 (1961) 35-50. 
  11. [11] Niethammer B., Derivation of the LSW-theory for Ostwald ripening by homogenization methods, Arch. Rat. Mech. Anal.147 (2) (1999) 119-178. Zbl0947.76092MR1702633
  12. [12] Niethammer B., Otto F., Ostwald Ripening: The screening length revisited, Calc. Var. and PDE13 (1) (2001) 33-68. Zbl0988.35021MR1854256
  13. [13] Niethammer B., Pego R.L., Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Stat. Phys.95 (5/6) (1999) 867-902. Zbl1005.82510MR1712441
  14. [14] Niethammer B., Pego R.L., On the initial-value problem in the Lifshitz–Slyozov–Wagner theory of Ostwald ripening, SIAM J. Math. Anal.31 (3) (2000) 457-485. Zbl0940.35133MR1735959
  15. [15] Nirenberg L., An extended interpolation inequality, Ann. Scuola Norm. Sup. Pisa Ser. III20 (1966) 733-737. Zbl0163.29905MR208360
  16. [16] Velázquez J.J.L., On the effect of stochastic fluctuations in the dynamics of the Lifshitz–Slyozov–Wagner model, J. Stat. Phys. (2000) 57-113. Zbl0973.82029MR1762657
  17. [17] Voorhees P.W., The theory of Ostwald ripening, J. Stat. Phys.38 (1985) 231-252. 
  18. [18] Wagner C., Theorie der Alterung von Niederschlägen durch Umlösen, Z. Elektrochemie65 (1961) 581-594. 
  19. [19] Ziemer W.P., Weakly Differentiable Functions, Springer, New York, 1989. Zbl0692.46022MR1014685

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.