What is it about?
If you have to free climb the Astronomy Tower and reach the top as quick as possible (will Draco appear and disarm Dumbledore?) then you should study calculus of variation. It connects variational problems in optimization with Muggles'toys called ODEs. Our paper is concerned with a long-standing question in which we look at a general class of ODEs and ask if they can be given a variational formulation, the so-called 'inverse problem'.
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Why is it important?
In other words, if the shortest way to the top is a spiral, am I still climbing Astronomy Tower or Azkaban Fortress? The 2nd order ODEs are settled, and we have developed a method for constructing the variational form for more complicated ODEs, namely those of 4th and higher order. Thus, we have made a key contribution to solving the 'inverse problem'. See you down the rabbit-hole in the quickest time.
Read the Original
This page is a summary of: On the inverse problem of calculus of variations for fourth-order equations, Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, March 2010, Royal Society Publishing,
DOI: 10.1098/rspa.2009.0618.
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