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(2013) Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Dordrecht, Springer.
Paul du Bois-Reymond (1879a,b) derived necessary conditions for only continuously differentiable extremals of J(y) = ∫ a b f(x, y(x), y"(x)) dx → extr. and was able to show that with this weakening of the conditions, there are no additional solutions. In 1904a, Zermelo generalizes du Bois-Reymond's result to higher derivatives. He gives two proofs. The second proof is close to that of du Bois-Reymond, which considers an isoperimetric variational problem, and is again presented with an altered conclusion based on an observation by Erhard Schmidt.
Publication details
DOI: 10.1007/978-3-540-70856-8_9
Full citation:
Thiele, R. (2013). Introductory note to 1904a, in Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Dordrecht, Springer, pp. 494-511.
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