Introductory note to 1904a
pp. 494-511
Abstrakt
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
Published in:
Zermelo Ernst (2013) Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik. Dordrecht, Springer.
Seiten: 494-511
DOI: 10.1007/978-3-540-70856-8_9
Referenz:
Thiele Rüdiger (2013) Introductory note to 1904a, In: Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Dordrecht, Springer, 494–511.