On a Cahn–Hilliard model for phase separation with elastic misfit

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1. [1] Barrett J.W., Blowey J.F., An error bound for the finite element approximation of the Cahn–Hilliard equation with logarithmic free energy, Numer. Math.72 (1995) 257-287. Zbl0851.65070MR1359705
2. [2] Barrett J.W., Blowey J.F., An error bound for the finite element approximation of a model for phase separation of a multi-component alloy, IMA J. Numer. Anal.16 (1996) 257-287. Zbl0849.65069MR1382718
3. [3] Bonetti E., Colli P., Dreyer W., Gilardi G., Schimperna G., Sprekels J., A solid-solid phase change model accounting for mechanical effects, Physica D165 (2002) 48-65. Zbl1008.74066MR1910617
4. [4] Cahn J.W., Hilliard J.E., Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys.28 (1958) 258-267. 
5. [5] Carrive M., Miranville A., Piétrus A., The Cahn–Hilliard equation for deformable elastic media, Adv. Math. Sci. Appl.10 (2000) 539-569. Zbl0987.35156MR1807441
6. [6] De Fontaine D., An analysis of clustering and ordering in multicomponent solid solutions – I. Stability criteria, J. Phys. Chem. Solids33 (1972) 287-310. 
7. [7] C.M. Elliott, The Cahn–Hilliard model for the kinetics of phase transitions, in: J.F. Rodrigues (ed.), Mathematical Models for Phase Change Problems, Internat. Ser. Numer. Math., vol. 88, Birkhäuser, Basel, pp. 35–73. Zbl0692.73003MR1038064
8. [8] C.M. Elliott, S. Luckhaus, A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy, SFB256 University Bonn, Preprint 195, 1991. 
9. [9] Eshelby J.D., Elastic inclusions and inhomogeneities, Prog. Solid Mech.2 (1961) 89-140. MR134510
10. [10] Fratzl P., Penrose O., Lebowitz J.L., Modelling of phase separation in alloys with coherent elastic misfit, J. Statist. Phys.95 (5/6) (1999) 1429-1503. Zbl0952.74052MR1712452
11. [11] H. Garcke, On mathematical models for phase separation in elastically stressed solids, habilitation thesis, 2000. 
12. [12] Garcke H., On Cahn–Hilliard sytems with elasticity, Proc. Roy. Soc. Edinburgh. Ser. A133 (2003) 307-331. Zbl1130.74037MR1969816
13. [13] Garcke H., Rumpf M., Weikard U., The Cahn–Hilliard equation with elasticity: finite element approximation and qualitative studies, Interfaces and Free Boundaries3 (2001) 101-118. Zbl0972.35164MR1805080
14. [14] Gehring F.W., The $L^p$-integrability of the partial derivatives of a quasi conformal mapping, Acta Math.130 (1973) 265-277. Zbl0258.30021MR402038
15. [15] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud., Princeton University Press, 1983. Zbl0516.49003MR717034
16. [16] Giaquinta M., Modica G., Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math.311/312 (1979) 145-169. Zbl0409.35015MR549962
17. [17] Hoyt J.J., The continuum theory of nucleation in multicomponent systems, Acta Metall.38 (1990) 1405-1412. 
18. [18] Khachaturyan A.G., Some questions concerning the theory of phase transitions in solids, Fiz. Tverd. Tela8 (1966) 2709-2717, English translation in, Sov. Phys. Solid. State8 (1966) 2163. 
19. [19] Kirkaldy J.S., Young D.J., Diffusion in the Condensed State, The Institute of Metals, London, 1987. 
20. [20] Larché F.C., Cahn J.W., Thermochemical equilibrium of multiphase solids under stress, Acta Metall.26 (1978) 1579-1589. 
21. [21] Larché F.C., Cahn J.W., The effect of self-stress on diffusion in solids, Acta Metall.30 (1982) 1835-1845. 
22. [22] Leo P.H., Lowengrub J.S., Jou H.J., A diffuse interface model for microstructural evolution in elastically stressed solids, Acta Mater.46 (1998) 2113-2130. 
23. [23] Novick–Cohen A., The Cahn–Hilliard equation: mathematical and modelling perspectives, Adv. Math. Sci. Appl.8 (1998) 965-985. Zbl0917.35044MR1657208
24. [24] Onsager L., Reciprocal relations in irreversible processes I, Phys. Rev.37 (1931) 405-426. Zbl0001.09501
25. [25] Onsager L., Reciprocal relations in irreversible processes II, Phys. Rev.38 (1931) 2265-2279. Zbl0004.18303
26. [26] Onuki A., Ginzburg–Landau approach to elastic effects in the phase separation of solids, J. Phys. Soc. Jpn.58 (1989) 3065-3068. 
27. [27] J.D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, Verhaendel. Kronik. Akad. Weten. Amsterdam, vol. 1 (1893) (in Dutch). 
28. [28] Zeidler E., Nonlinear Functional Analysis and its Applications IV, Springer, New York, 1988. Zbl0648.47036MR932255