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- W2033647961 abstract "We consider a calculus of variations problem of minimizing a function a of integrals whose integrands/* depend on x, y, and functions w'(x, y), z(x1 y), and their first partial derivatives, and possibly also on their mixed second partial derivatives dw'/dxdy, dz/dxdy. The functions w' and z defining admissible surfaces are restricted to be absolutely continuous in the sense of Vitali, and also in the sense of Tonelli, and moreover to have uniform bounds for the partial derivatives which actually enter. The functions z are required to take fixed boundary values on the region G2 of the ;ry-plane which is the domain of integration. The functions w', on the other hand, are restricted only by assigned initial values on two lines x — x and y = y which lie in G2 or on its boundary. For convenience we may suppose x — y = 0. Admissible surfaces are also required to give prescribed values to certain functions /3 of the integrals J and to satisfy almost everywhere on G2 a set of partial differential equations" @default.
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- W2033647961 date "1959-11-01" @default.
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- W2033647961 title "A multiplier rule for a class of two-dimensional variational problems" @default.
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- W2033647961 doi "https://doi.org/10.1090/s0002-9904-1959-10382-7" @default.
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