Abstract
The Euler-Lagrange calculus was created to determine extremals of functionals. If the solution of the Euler-Lagrange equation is unique among all admitted functions, then physical or geometric insights into the problem might lead to the conclusion that it is indeed the desired extremal. In addition, the second variation provides necessary and also sufficient conditions on extremals.
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Kielhöfer, H. (2018). Direct Methods in the Calculus of Variations. In: Calculus of Variations. Texts in Applied Mathematics, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-319-71123-2_3
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DOI: https://doi.org/10.1007/978-3-319-71123-2_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-71123-2
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