Abstract
The formula for the variation of a functional is obtained where the integrand depends on several independent variables x j, several functions of these variables u k and a finite number of partial derivatives of any order of the functions u k with respect to x j. Besides the functions u k, the boundary of the domain can also move. The formula generalizes the well-known case when only first-order partial derivatives are admitted.
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References
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Dickey, L.A. On the Variation of a Functional when the Boundary of the Domain is not Fixed. Lett Math Phys 83, 33–40 (2008). https://doi.org/10.1007/s11005-007-0198-3
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DOI: https://doi.org/10.1007/s11005-007-0198-3