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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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MathSciNet review: 1181197

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Book Information

Author(s): R. Dobrushin, R. Kotecky, and S. Shlosman
Title: Wulff construction, A global shape from local interaction
Additional book information: American Mathematical Society, Providence, RI, 1992, ix + 204 pp., US$130.00. ISBN 0-8218-4563-2


References:

Bibliography

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B. Dacorogna and C. E. Pfister, Wulff theorem and best constant in Sobolev inequality, J. Math. Pures Appl. (9) 71 (1992), 97-118. MR 1170247 (94d:49070)

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A. Dinghas, Über einen Geometrischen Satz von Wulff fur die Gleichgewichtsform von Kristallen, Z. Kristall 105 (1944), 304-314 MR 0012454 (7:25d)

[F]
I. Fonseca, The Wulff theorem revisited, Proc. Roy. Soc. London Ser. A 432 (1991), 125-145. MR 1116536 (92e:49053)

[FM]
I. Fonseca and S. Muller, A uniqueness proof for the Wulff problem, Proc. Edinburgh Math. Soc. 119A (1991), 125-136. MR 1130601 (93c:49026)

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M. Gage, Evolving plane curves by curvature in relative geometries, Duke Math. J. 72 (1993), 441-466. MR 1248680 (94j:53001)

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C. Herring, The use of classical macroscopic concepts in surface energy problems, Structure and Properties of Solid Surfaces (R. Gomer, ed.), Univ. of Chicago Press, Chicago, 1952, pp. 5-73; Some theorems on the free energy of crystal surfaces, Phys. Rev. 28 (1951), 87-93.

[KS]
M. Katsoulakis and P. E. Souganidis, Interacting particle systems and generalized evolution of fronts, Arch. Rational Mech. Anal. (in preparation). MR 1288808 (95h:82023)

[M]
F. Morgan, Geometric measure theory. A beginner's guide, Academic Press, New York, 1988. MR 933756 (89f:49036)

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C. E. Pfister, Long deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta 64 (1991), 953-1054. MR 1149430 (93c:82011)

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R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970. MR 0274683 (43:445)

[T]
J. E. Taylor, Existence and structure of solutions to a class of nonelliptic variational problems, Sympos. Math., vol. 14, Academic Press, London, 1974, pp. 499-508; Unique structure of solutions to a class of nonelliptic variational problems, Proc. Sympos. Pure Math., vol. XXVII, Amer. Math. Soc., Providence, RI, 1974, pp. 481-489. MR 0420407 (54:8421)

[TCH]
J. E. Taylor, J. W. Cahn, and C. A. Handwerker, Geometric models of crystal growth, Acta Met. Mat. 40 (1992), 1443-1474.

[W]
G. Wulff, Zur frage der Geschwindigkeit des Wachstums und der Auflosung der Krystal-flachen, Z. Krist. 34 (1901), 449.


Additional Information:

Reviewer(s):
Jean E. Taylor

Review Information:
Journal: Bull. Amer. Math. Soc. 31 (1994), 291-296.
DOI: 10.1090/S0273-0979-1994-00535-X
PII: S 0273-0979(1994)00535-X




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