Book Review
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A. V. Bäcklund, Ueber Flächentransformationen, Math. Ann. 9 (1875), no. 3, 297–320 (German). MR 1509862, DOI 10.1007/BF01443337
Erich Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik, Math. Ann. 84 (1921), no. 3-4, 258–276 (German). MR 1512036, DOI 10.1007/BF01459410
Courant, R., and Hilbert, D., Methoden der Mathematischen Physik, J. Springer, Berlin, 1924; English translation: Methods of Mathematical Physics, Interscience Publ., New York, 1953.
Olivier Darrigol, The spirited horse, the engineer, and the mathematician: water waves in nineteenth-century hydrodynamics, Arch. Hist. Exact Sci. 58 (2003), no. 1, 21–95. MR 2020055, DOI 10.1007/s00407-003-0070-5
Elkana, Y., The Discovery of the Conservation of Energy, Hutchinson Educational Ltd., London, 1974.
J. D. Eshelby, The force on an elastic singularity, Philos. Trans. Roy. Soc. London Ser. A 244 (1951), 84–112. MR 48294, DOI 10.1098/rsta.1951.0016
E. L. Hill, Hamilton’s principle and the conservation theorems of mathematical physics, Rev. Modern Physics 23 (1951), 253–260. MR 0044959, DOI 10.1103/revmodphys.23.253
J. K. Knowles and Eli Sternberg, On a class of conservation laws in linearized and finite elastostatics, Arch. Rational Mech. Anal. 44 (1971/72), 187–211. MR 337111, DOI 10.1007/BF00250778
Robert M. Miura, Clifford S. Gardner, and Martin D. Kruskal, Korteweg-de Vries equation and generalizations. II. Existence of conservation laws and constants of motion, J. Mathematical Phys. 9 (1968), 1204–1209. MR 252826, DOI 10.1063/1.1664701
Neuenschwander, D.E., Emmy Noether’s Wonderful Theorem, The Johns Hopkins University Press, Baltimore, MD, 2011.
Noether, E., Invariante Variationsprobleme, Nachr. König. Gesell. Wissen. Göttingen, Math.–Phys. Kl. (1918), 235–257.
Peter J. Olver, Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics, Arch. Rational Mech. Anal. 85 (1984), no. 2, 131–160. MR 731282, DOI 10.1007/BF00281448
Peter J. Olver, Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rational Mech. Anal. 102 (1988), no. 2, 167–181. MR 943430, DOI 10.1007/BF00251497
Peter J. Olver, Applications of Lie groups to differential equations, 2nd ed., Graduate Texts in Mathematics, vol. 107, Springer-Verlag, New York, 1993. MR 1240056, DOI 10.1007/978-1-4612-4350-2
Olver, P.J., Recent advances in the theory and application of Lie pseudo-groups, in: XVIII International Fall Workshop on Geometry and Physics, M. Asorey, J.F. Cariñena, J. Clemente–Gallardo, and E. Martínez, eds., AIP Conference Proceedings, vol. 1260, American Institute of Physics, Melville, NY, 2010, pp. 35–63.
S. I. Pohožaev, On the eigenfunctions of the equation $\Delta u+\lambda f(u)=0$, Dokl. Akad. Nauk SSSR 165 (1965), 36–39 (Russian). MR 0192184
Patrizia Pucci and James Serrin, A general variational identity, Indiana Univ. Math. J. 35 (1986), no. 3, 681–703. MR 855181, DOI 10.1512/iumj.1986.35.35036
Rice, J.R., A path-independent integral and the approximate analysis of strain concentrations by notches and cracks, J. Appl. Mech. 35 (1968), 376–386.
R. C. A. M. Van der Vorst, Variational identities and applications to differential systems, Arch. Rational Mech. Anal. 116 (1992), no. 4, 375–398. MR 1132768, DOI 10.1007/BF00375674
References
- Bäcklund, A.V., Ueber Flachentransformationen, Math. Ann. 9 (1876), 297–320. MR 1509862
- Bessel-Hagen, E., Über die Erhaltungssätze der Elektrodynamik, Math. Ann. 84 (1921), 258–276. MR 1512036
- Courant, R., and Hilbert, D., Methoden der Mathematischen Physik, J. Springer, Berlin, 1924; English translation: Methods of Mathematical Physics, Interscience Publ., New York, 1953.
- Darrigol, O., The spirited horse, the engineer, and the mathematician: water waves in nineteenth-century hydrodynamics, Arch. Hist. Exact Sci. 58 (2003), 21–95. MR 2020055 (2004k:76002)
- Elkana, Y., The Discovery of the Conservation of Energy, Hutchinson Educational Ltd., London, 1974.
- Eshelby, J.D., The force on an elastic singularity, Phil. Trans. Roy. Soc. London A 244 (1951), 57–112. MR 0048294 (13:1007e)
- Hill, E.L., Hamilton’s principle and the conservation theorems of mathematical physics, Rev. Mod. Phys. 23 (1951), 253–260. MR 0044959 (13:503g)
- Knowles, J.K., and Sternberg, E., On a class of conservation laws in linearized and finite elastostatics, Arch. Rat. Mech. Anal. 44 (1972), 187–211. MR 0337111 (49:1883)
- Miura, R.M., Gardner, C.S., and Kruskal, M.D., Korteweg–deVries equation and generalizations. II. Existence of conservation laws and constants of the motion, J. Math. Phys. 9 (1968), 1204–1209 MR 0252826 (40:6042b)
- Neuenschwander, D.E., Emmy Noether’s Wonderful Theorem, The Johns Hopkins University Press, Baltimore, MD, 2011.
- Noether, E., Invariante Variationsprobleme, Nachr. König. Gesell. Wissen. Göttingen, Math.–Phys. Kl. (1918), 235–257.
- Olver, P.J., Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics, Arch. Rat. Mech. Anal. 85 (1984), 131–160. MR 731282 (85i:73010b)
- Olver, P.J., Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rat. Mech. Anal. 102 (1988), 167–181. MR 943430 (89m:73014)
- Olver, P.J., Applications of Lie Groups to Differential Equations, First Edition, Springer–Verlag, New York, 1986; Second Edition, Springer–Verlag, New York, 1993. MR 1240056 (94g:58260)
- Olver, P.J., Recent advances in the theory and application of Lie pseudo-groups, in: XVIII International Fall Workshop on Geometry and Physics, M. Asorey, J.F. Cariñena, J. Clemente–Gallardo, and E. Martínez, eds., AIP Conference Proceedings, vol. 1260, American Institute of Physics, Melville, NY, 2010, pp. 35–63.
- Pohožaev, S.I., On the eigenfunctions of the equation $\Delta u+\lambda f(u)=0$, Soviet Math. Dokl. 6 (1965), 1408–1411. MR 0192184 (33:411)
- Pucci, P., and Serrin, J., A general variational identity, Indiana Univ. Math. J. 35 (1986), 681–703. MR 855181 (88b:35072)
- Rice, J.R., A path-independent integral and the approximate analysis of strain concentrations by notches and cracks, J. Appl. Mech. 35 (1968), 376–386.
- van der Vorst, R.C.A.M., Variational identities and applications to differential systems, Arch. Rat. Mech. Anal. 116 (1991), 375–398. MR 1132768 (93d:35043)
Review Information:
Reviewer:
Peter J. Olver
Affiliation:
Minneapolis, Minnesota
Email:
olver@umn.edu
Journal:
Bull. Amer. Math. Soc.
50 (2013), 161-167
DOI:
https://doi.org/10.1090/S0273-0979-2011-01364-7
Published electronically:
November 4, 2011
Review copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
