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Thread: Hilbret's 23rd Problem

  1. #1 Hilbret's 23rd Problem 
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    In his twenty-third problem David Hilbret suggests further developing the calculus of variations. This is a subject that I have not studied yet, and would like to ask those more familiar with it than I what it lacks in development as opposed to calculus of one variable or calculus of several variables.


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  3. #2 Re: Hilbret's 23rd Problem 
    . DrRocket's Avatar
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    Quote Originally Posted by Ellatha
    In his twenty-third problem David Hilbret suggests further developing the calculus of variations. This is a subject that I have not studied yet, and would like to ask those more familiar with it than I what it lacks in development as opposed to calculus of one variable or calculus of several variables.
    Hilbert's 23rd problem was rather open-ended, unlike the others. It is sufficiently open-ended that one could never claim to have solved it.

    There has been quite a bit done with the calculus of variations and minimization problems since Hilbert's address was given in 1900.

    There is a nice discussion by Guido Stampacchia in the "Proceedings of Symposia in Pure Mathematics, Vol XXVII, Part 2, Mathematical developments arising from Hilbert Problems".

    One can consider the entire field of optimal control, including the Pontryagin Maximal Principal as an extension of the calculus of variations. Bliss, at The University of Chicago, did work that forshadowed Pontryagin, but it was not widely known at the time.


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