Geodesic
Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 4, pp. 422-432.

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For variational functionals in Sobolev spaces $\{W^{1,p}\}\;(1\leq p\infty)$ we introduce a sequence of so-called dominant “growth estimates” for the gradient of appropriate order of the integrand, each of which guarantees the appropriate level of smoothness of variational functional in the $C^{1}$-smooth points of the Sobolev space. Earlier studied K-pseudopolynomial representations of the integrand are particular cases of dominant growth estimates. However, unlike the pseudopolynomial case $(p\in \mathbb{N})$, our approach enables us to consider variational problems on the complete Sobolev scale $(1\leq p\infty)$. 
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I. V. Orlov; I. A. Romanenko. Dominant integrands growth estimates and smoothness of variational functionals in Sobolev spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 4, pp. 422-432. http://geodesic.mathdoc.fr/item/ISU_2015_15_4_a6/

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