Geodesic
Compact-analytical properties of variational functional in Sobolev spaces~$W^{1,p}$
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 94-119.

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In the work, conditions of welldefiniteness, compact continuity, compact differentiability and multiple compact differentiability of the Euler–Lagrange one-dimensional variational functional in Sobolev–Bochner spaces $W^{1,p}([a;b],F)$ are obtained in terms of belonging of the integrand to the corresponding Weierstrass pseudopolynomial classes. 
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I. V. Orlov. Compact-analytical properties of variational functional in Sobolev spaces~$W^{1,p}$. Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 94-119. http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a6/

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