Correctors and error estimates in the homogenization of a Mullins-Sekerka problem
Garroni, Adriana ; Niethammer, Barbara
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 371-393 / Harvested from Numdam
Publié le : 2002-01-01
@article{AIHPC_2002__19_4_371_0,
     author = {Garroni, Adriana and Niethammer, Barbara},
     title = {Correctors and error estimates in the homogenization of a Mullins-Sekerka problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {19},
     year = {2002},
     pages = {371-393},
     zbl = {1003.82007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2002__19_4_371_0}
}
Garroni, Adriana; Niethammer, Barbara. Correctors and error estimates in the homogenization of a Mullins-Sekerka problem. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) pp. 371-393. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_4_371_0/

[1] Alikakos N., Fusco G., The equations of Ostwald ripening for dilute systems, J. Stat. Phys. 95 (5/6) (1999) 851-866. | MR 1712440 | Zbl 0952.76089

[2] Alikakos N., Fusco G., Ostwald ripening for dilute systems under quasistationary dynamics, Comm. Math. Phys., to appear. | MR 1993380 | Zbl 1082.82005

[3] Chen X., Global asymptotic limit of solutions of the Cahn-Hilliard equation, J. Diff. Geometry 44 (1996) 262-311. | MR 1425577 | Zbl 0874.35045

[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. | MR 1421209 | Zbl 0884.35177

[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. | MR 1493040 | Zbl 0912.35020

[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. | MR 1456181 | Zbl 0880.35140

[7] Grisvard P., Elliptic Problems in Nonsmoooth Domains, Pitman, Boston, 1985. | MR 775683 | Zbl 0695.35060

[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. | MR 1034024 | Zbl 0687.35007

[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] Lifshitz I.M., Slyozov V.V., The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35-50.

[11] Niethammer B., Derivation of the LSW-theory for Ostwald ripening by homogenization methods, Arch. Rat. Mech. Anal. 147 (2) (1999) 119-178. | MR 1702633 | Zbl 0947.76092

[12] Niethammer B., Otto F., Ostwald Ripening: The screening length revisited, Calc. Var. and PDE 13 (1) (2001) 33-68. | MR 1854256 | Zbl 0988.35021

[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. | MR 1712441 | Zbl 1005.82510

[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. | MR 1735959 | Zbl 0940.35133

[15] Nirenberg L., An extended interpolation inequality, Ann. Scuola Norm. Sup. Pisa Ser. III 20 (1966) 733-737. | Numdam | MR 208360 | Zbl 0163.29905

[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. | MR 1762657 | Zbl 0973.82029

[17] Voorhees P.W., The theory of Ostwald ripening, J. Stat. Phys. 38 (1985) 231-252.

[18] Wagner C., Theorie der Alterung von Niederschlägen durch Umlösen, Z. Elektrochemie 65 (1961) 581-594.

[19] Ziemer W.P., Weakly Differentiable Functions, Springer, New York, 1989. | MR 1014685 | Zbl 0692.46022