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Crystalline variational problems
Author(s):
Jean E.
Taylor
Journal:
Bull. Amer. Math. Soc.
84
(1978),
568-588.
MSC (1970):
Primary 49F22, 49F20, 53C65, 49D99, 82A60, 82A65, 52A05, 52A40, 28A75, 49F10
MathSciNet review:
0493671
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Additional information
References:
- [Ad] W. K. Allard, On the first variation of a varifold, Ann. of Math. 95 (1972), 417-491. MR 307015
- [Al] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. of Math. 87 (1968), 321-391. MR 225243
- [A2] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. No. 165, 1976. MR 420406
- [AC] E. Arbel and J. W. Cahn, A method for the absolute measurement of anisotropic solid-melt surface free energies (preprint).
- [C] J. W. Cahn, personal communication.
- [D] A. Dinghas, Über einen geometrischen Satz von Wulff für die Gleichgewichtsform von Kristallen, Zeitschrift für Kristallographie 105 (1944), 304-314. MR 12454
- [F1] H. Federer, Geometric measure theory, Springer-Verlag, New York, 1969. MR 257325
- [F2] H. Federer, Colloquium lectures on geometric measure theory, Summer Meeting of the Amer. Math. Soc. (Seattle, Washington, August 15-18, 1977), Bull. Amer. Math. Soc. 84 (1978), 291-338. MR 467473
- [Fu] J. H. G. Fu, A mathematical model for crystal growth and related problems, Junior paper, Princeton University.
- [H] C. Herring, Some theorems on the free energy of crystal surface, Phys. Rev. 82 (1951), 87-93.
- [Le] M. v. Laue, Der Wulffsche Satz für die Gleichgewichtsform von Kristallen, Zeitschrift für Kristallographie 105 (1943), 124-133.
- [Ln] H. Liebmann, Der Curie-Wulff'sche Satz über Combinationsformen von Krystallen, Zeitschrift für Krystallographie und Mineralogie 53 (1914), 171-177.
- [P] H. R. Parks, Explicit determination of area minimizing hypersurfaces, Duke Math. J. 44 (1977), 519-534. MR 458304
- [R] R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N. J., 1970. MR 274683
- [T1] J. E. Taylor, Existence and structure of solutions to a class of nonelliptic variational problems, Symposia Mathematica 14 (1974), 499-508. MR 420407
- [T2] J. E. Taylor, Unique structure of solutions to a class of nonelliptic variational problems, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R.I., 1974, pp. 481-489. MR 388225
- [W] G. Wulff, Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflachen, Zeitschrift für Krystallographie und Mineralogie 34 (1901), 449-530.
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49F22, 49F20, 53C65, 49D99, 82A60, 82A65, 52A05, 52A40, 28A75, 49F10
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49F22, 49F20, 53C65, 49D99, 82A60, 82A65, 52A05, 52A40, 28A75, 49F10
Additional Information:
DOI:
10.1090/S0002-9904-1978-14499-1
PII:
S 0002-9904(1978)14499-1
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