Book Review
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MathSciNet review:
1568147
Full text of review:
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Book Information:
Author:
Gianni Dal Maso
Title:
An introduction to $\Gamma $-convergence
Additional book information:
Birkh\"auser, Boston, 1992, xiv+337 pp., US$69.50. ISBN 0-8176-3679-X.
J. R. Baxter and N. C. Jain, Asymptotic capacities for finely divided bodies and stopped diffusions, Illinois J. Math. 31 (1987), no. 3, 469–495. MR 892182
Alain Bensoussan, Jacques-Louis Lions, and George Papanicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications, vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503330
Gunduz Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), no. 3, 205–245. MR 816623, DOI 10.1007/BF00254827
D. Cioranescu and F. Murat, Un terme étrange venu d’ailleurs, Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. II (Paris, 1979/1980) Res. Notes in Math., vol. 60, Pitman, Boston, Mass.-London, 1982, pp. 98–138, 389–390 (French, with English summary). MR 652509
Gianni Dal Maso and Umberto Mosco, Wiener’s criterion and $\Gamma$-convergence, Appl. Math. Optim. 15 (1987), no. 1, 15–63. MR 866165, DOI 10.1007/BF01442645
[6] E. De Giorgi, 
-convergenza e G-convergenza, Boll. Un. Mat. Ital. (5) (1977), 213-220.
Robert V. Kohn and Peter Sternberg, Local minimisers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 1-2, 69–84. MR 985990, DOI 10.1017/S0308210500025026
Robert V. Kohn and Gilbert Strang, Optimal design and relaxation of variational problems. I, Comm. Pure Appl. Math. 39 (1986), no. 1, 113–137. MR 820342, DOI 10.1002/cpa.3160390107
Luciano Modica, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal. 98 (1987), no. 2, 123–142. MR 866718, DOI 10.1007/BF00251230
François Murat, Un contre-exemple pour le problème du contrôle dans les coefficients, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A708–A711 (French). MR 288651
G. C. Papanicolaou and S. R. S. Varadhan, Diffusion in regions with many small holes, Stochastic differential systems (Proc. IFIP-WG 7/1 Working Conf., Vilnius, 1978) Lecture Notes in Control and Information Sci., vol. 25, Springer, Berlin-New York, 1980, pp. 190–206. MR 609184
Jeffrey Rauch and Michael Taylor, Electrostatic screening, J. Mathematical Phys. 16 (1975), 284–288. MR 382834, DOI 10.1063/1.522539
Enrique Sánchez-Palencia, Nonhomogeneous media and vibration theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Berlin-New York, 1980. MR 578345
Peter Sternberg, The effect of a singular perturbation on nonconvex variational problems, Arch. Rational Mech. Anal. 101 (1988), no. 3, 209–260. MR 930124, DOI 10.1007/BF00253122
- [1]
- J. Baxter and N. Jain, Asymptotic capacities for finely divided bodies and stopped diffusions, Illinois J. Math. 31 (1987), 469-495. MR 892182 (88m:60205)
- [2]
- A. Bensoussan, J. L. Lions, and G. C. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. MR 503330 (82h:35001)
- [3]
- G. Caginalp, An analysis of a phase-field model of a free boundary, Arch. Rational Mech. Anal. 92 (1986), 108. MR 816623 (87c:80011)
- [4]
- D. Cioranescu and F. Murat, Un terme étrange venu dàilleurs. I, II, Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar, Vol. II, Pitman, London, 1982, pp. 98-138. MR 652509 (84e:35039a)
- [5]
- G. Dal Maso and U. Mosco, Wiener's criterion and
-convergence, Appl. Math. Optim. 15 (1987), 15-63. MR 866165 (88e:49031)
- [6]
- E. De Giorgi, -convergenza e G-convergenza, Boll. Un. Mat. Ital. (5) (1977), 213-220.
- [7]
- R. V. Kohn and P. Sternberg, Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A (1989), 69-84. MR 985990 (90c:49021)
- [8]
- R. V. Kohn and G. Strang, Optimal design and relaxation of variational problems. I, II, and III, Comm. Pure Appl. Math. 39 (1986), 113-137, 139-182, 353-377. MR 820342 (87d:49019a)
- [9]
- L. Modica, The gradient theory of phase-transitions and the minimal interface criterion, Arch. Rational Mech. Anal. 98 (1987), 123-142. MR 866718 (88f:76038)
- [10]
- F. Murat, Un contre-exemple pour le probleme du controle dans les coefficients, C. R. Acad. Sci. Paris A 273 (1971), 708-711. MR 0288651 (44:5847)
- [11]
- G. C. Papanicolaou and S. R. S. Varadhan, Diffusion in regions with many small holes, Stochastic Differential Systems, Filtering and Control, Lecture Notes in Control and Inform. Sci., vol. 25, Springer-Verlag, Berlin, 1980, pp. 190-206. MR 609184 (84f:60110)
- [12]
- J. Rauch and M. Taylor, Electrostatic screening, J. Math. Phys. 16 (1975), 284-288. MR 0382834 (52:3716)
- [13]
- E. Sanchez-Palencia, Non-homogeneous media and vibration theory, Lecture Notes in Phys., vol. 127, Springer-Verlag, Berlin, 1980. MR 578345 (82j:35010)
- [14]
- P. Sternberg, The effect of a singular perturbation on nonconvex variational problems, Arch. Rational Mech. Anal. 101 (1988), 209-260. MR 930124 (89h:49007)
Review Information:
Reviewer:
Marco Avellaneda
Journal:
Bull. Amer. Math. Soc.
31 (1994), 277-283
DOI:
https://doi.org/10.1090/S0273-0979-1994-00532-4
