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Bolza Problem

Given the functional

U=int_(t_0)^(t_1)f(y_1,...,y_n;y_1^',...,y_n^')dt+G(y_(10),...,y_(nr);y_(11),...,y_(n1)),
(1)

find in a class of arcs satisfying p differential and q finite equations

phi_alpha(y_1,...,y_n;y_1^',...,y_n^')=0 for alpha=1,...,p psi_beta(y_1,...,y_n)=0 for beta=1,...,q
(2)

as well as the r equations on the endpoints

chi_gamma(y_(10),...,y_(nr);y_(11),...,y_(n1))=0 for gamma=1,...,r,
(3)

which renders U a minimum.

See also

Calculus of Variations

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References

Goldstine, H. H. A History of the Calculus of Variations from the 17th through the 19th Century. New York: Springer-Verlag, p. 374, 1980.

Referenced on Wolfram|Alpha

Bolza Problem

Cite this as:

Weisstein, Eric W. "Bolza Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BolzaProblem.html

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