Mathematical existence of crystal growth with Gibbs-Thomson curvature effects

Journal of Geometric Analysis

Volumn 10, Issue 1, 2000, Pages

  Almgren, Fred ^a   Wang, Lihe ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001861231     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02921806     Document Type: Article

References (22)

1. W.K. Allard 1972 On the first variation of a varifold Ann. Math. 95 418 491 307015 10.2307/1970868
2. F. Almgren 1976 Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints Mem. Am. Math. Soc 165 199 + vii 199 + vii 420406
3. F. Almgren E.H. Lieb 1989 Symmetric decreasing rearrangement is sometimes continuous J. Am. Math. Soc. 2 683 773 10.2307/1990893 1002633 0688.46014
4. F. Almgren R. Schoen L. Simon 1977 Regularity and singularity estimates for hypersurfaces minimizing parametric elliptic variational integrals Acta Math. 139 218 265 467476
5. F. Almgren J. Taylor L. Wang 1993 Curvature driven flows: A variational approach SIAMJ. Control and Optimization 31 387 438 10.1137/0331020 1205983 0783.35002
6. R. Almgren 1993 Variational algorithms and pattern formation in dendritic solidification J. Comp. Phys. 106 337 354 1218734 0787.65095
7. Birkhoff, G. and Rota, G.-C.Ordinary Differential Equations, Blaisdell Pub. Co., Waltham, MA, 1969.
8. E. Bombieri 1982 Regularity theory for almost minimal currents Arch. Rational Mech. Anal 78 99 130 10.1007/BF00250836 648941 0485.49024
9. J.W. Cahn C.A. Handwerker J.E. Taylor 1992 Geometric models of crystal growth Acta Metall. Matr. 40 1443 1474 10.1016/0956-7151(92)90090-2
10. 2,θ (Ω.δ) Annali di Matematica Pura ed Applicata 73 55 102 10.1007/BF02415082 213737 0144.14101
11. Federer, H.Geometric Measure Theory, Springer-Verlag, New York, 1969.
12. Gilbarg, D. and Trudinger, N.S.Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1970.
13. Gurtin, M. Thermomechanics of evolving phase boundaries, preprint.
14. Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural'ceva, N.N.Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, vol. 23,Am. Math. Soc, Providence, RI, 1968.
15. S. Luckhaus 1990 Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature Euro. J. Applied Math. 1 101 111 1117346 0734.35159
16. Morrey, Jr., C.B.Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966.
17. Pazy, A.Semi-groups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences,49, Springer-Verlag, New York, 1983.
18. Rachev, S.T. The Monge-Kantorovitch mass transference problem and its stochastic applications,Theor. Prob. Appl.,XXIX, 647-676.
19. Roosen, A.R. Modeling crystal growth in a diffusion field with fully-facetted crystals, Ph.D. thesis, Rutgers University, New Jersey, 1993.
20. Rubinstein, Z.A Course in Ordinary and Partial Differential Equations, Academic Press, New York, 1969.
21. Stein, E.M.Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, Princeton University Press, Princeton, NJ, 1970.
22. Yosida, K.Functional Analysis, 4th ed., Springer-Verlag, New York, 1974.