Abstract
By E. Noether’s famous theorem, if an integral in the calculus of variations has continuous one-parameter groups of symmetries, then a conservation law, or a first integral of the Euler-Lagrange equation for the integral, must be associated to each of such symmetries. A concrete stress-energy tensor for smooth maps has been found by P. Baird and J. Eells, who also explained its applications in the theory of harmonic maps [B-E]. This chapter is devoted to the relevant topics.
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© 1996 Birkhäuser Boston
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Xin, Y. (1996). Conservation Law. In: Geometry of Harmonic Maps. Progress in Nonlinear Differential Equations and Their Applications, vol 23. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4084-6_2
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DOI: https://doi.org/10.1007/978-1-4612-4084-6_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8644-8
Online ISBN: 978-1-4612-4084-6
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