Book Review
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MathSciNet review:
1568015
Full text of review:
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Book Information:
Author:
Michael Struwe
Title:
Variational methods (Applications to nonlinear PDE and Hamiltonian systems)
Additional book information:
Springer-Verlag, New York, 1990, 244 pp., US$39.50. ISBN 3-540-52022-8.
[A1] S. I. Al'ber, On n-dimensional problems in the calculus of variations in the large, Soviet Math. Dokl. 5 (1964), 700-704.
[A2] -, Spaces of mappings into a manifold with negative curvature, Soviet Math. Dokl. 9 (1967), 6-9.
V. Bangert, Geodätische Linien auf Riemannschen Mannigfaltigkeiten, Jahresber. Deutsch. Math.-Verein. 87 (1985), no. 2, 39–66 (German). MR 789708
Philippe G. Ciarlet, Mathematical elasticity. Vol. I, Studies in Mathematics and its Applications, vol. 20, North-Holland Publishing Co., Amsterdam, 1988. Three-dimensional elasticity. MR 936420
[CDY] K. C. Chang, W. Y. Ding, and R. Ye, Finite-time blow-up of the heat flow of harmonic maps from surfaces.
Bernard Dacorogna, Direct methods in the calculus of variations, Applied Mathematical Sciences, vol. 78, Springer-Verlag, Berlin, 1989. MR 990890, DOI 10.1007/978-3-642-51440-1
James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
Mariano Giaquinta and Enrico Giusti, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31–46. MR 666107, DOI 10.1007/BF02392725
Jürgen Jost, Two-dimensional geometric variational problems, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1991. A Wiley-Interscience Publication. MR 1100926
Wilhelm Klingenberg, Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, Vol. 230, Springer-Verlag, Berlin-New York, 1978. MR 0478069
Luc Lemaire, Applications harmoniques de surfaces riemanniennes, J. Differential Geometry 13 (1978), no. 1, 51–78 (French). MR 520601
J. Sacks and K. Uhlenbeck, The existence of minimal immersions of $2$-spheres, Ann. of Math. (2) 113 (1981), no. 1, 1–24. MR 604040, DOI 10.2307/1971131
Richard Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), no. 2, 479–495. MR 788292
Richard Schoen and Karen Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geometry 17 (1982), no. 2, 307–335. MR 664498
R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332, DOI 10.2307/1971247
[St] M. Struwe, Plateau's problem and the calculus of variations, Princeton Univ. Press, Princeton, NJ, 1989.
Henry C. Wente, Large solutions to the volume constrained Plateau problem, Arch. Rational Mech. Anal. 75 (1980/81), no. 1, 59–77. MR 592104, DOI 10.1007/BF00284621
Eberhard Zeidler, Nonlinear functional analysis and its applications. IV, Springer-Verlag, New York, 1988. Applications to mathematical physics; Translated from the German and with a preface by Juergen Quandt. MR 932255, DOI 10.1007/978-1-4612-4566-7
- [A1]
- S. I. Al'ber, On n-dimensional problems in the calculus of variations in the large, Soviet Math. Dokl. 5 (1964), 700-704.
- [A2]
- -, Spaces of mappings into a manifold with negative curvature, Soviet Math. Dokl. 9 (1967), 6-9.
- [B]
- V. Bangert, Geodätische Linien auf Riemannschen Mannigfaltigkeiten, Jber. DMV 87 (1985), 39-66. MR 789708 (87i:58036)
- [C]
- Ph. Ciarlet, Mathematical elasticity, vol. I: Three-dimensional elasticity, North-Holland, Amsterdam, 1988. MR 936420 (89e:73001)
- [CDY]
- K. C. Chang, W. Y. Ding, and R. Ye, Finite-time blow-up of the heat flow of harmonic maps from surfaces.
- [D]
- B. Dacorogna, Direct methods in the calculus of variations, Springer-Verlag, New York, 1989. MR 990890 (90e:49001)
- [ES]
- J. Eells and J. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1986), 109-160. MR 0164306 (29:1603)
- [GG]
- M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. MR 666107 (84b:58034)
- [J]
- J. Jost, Two-dimensional geometric variational problems, Wiley-Interscience, Chichester, 1991. MR 1100926 (92h:58045)
- [K]
- W. Klingenberg, Lectures on closed geodesies, Springer-Verlag, New York, 1978. MR 0478069 (57:17563)
- [L]
- L. Lemaire, Applications harmoniques de surfaces riemanniennes, J. Differential Geom. 13 (1978), 51-78. MR 520601 (80h:58024)
- [SaU]
- J. Sacks and K. Uhlenbeck, On the existence of minimal immersions of 2-spheres, Ann. of Math. (2) 113 (1981), 1-24. MR 604040 (82f:58035)
- [S]
- R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495. MR 788292 (86i:58137)
- [SU]
- R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335; Correction in J. Differential Geom. 18 (1983), 329. MR 664498 (84b:58037a)
- [Sy]
- R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math. (2) 110 (1979), 127-142. MR 541332 (81k:58029)
- [St]
- M. Struwe, Plateau's problem and the calculus of variations, Princeton Univ. Press, Princeton, NJ, 1989.
- [W]
- H. Wente, Large solutions to the volume constrained Plateau problem, Arch. Rational Mech. Anal. 75 (1980), 59-77. MR 592104 (82a:49049)
- [Z]
- E. Zeidler, Nonlinear functional analysis and its applications, vol. IV: Applications to mathematical physics, Springer-Verlag, New York, 1988. MR 932255 (90b:00004)
Review Information:
Reviewer:
J"urgen Jost
Journal:
Bull. Amer. Math. Soc.
28 (1993), 149-153
DOI:
https://doi.org/10.1090/S0273-0979-1993-00339-2
