Geodesic
Functionals with the $H$-property in the Sobolev space~$W_1^1$
Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 879-896

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Special classes of convex functionals in the Sobolev space $W_1^1$ are under consideration. Functionals in these classes are shown to have the so-called $H$-property: if a sequence of points in the domain of a functional converges weakly and the values of the functional at these points converge, then this sequence converges strongly in $W_1^1$. 
@article{SM_2004_195_6_a5,
     author = {A. S. Leonov},
     title = {Functionals with the $H$-property in the {Sobolev} space~$W_1^1$},
     journal = {Sbornik. Mathematics},
     pages = {879--896},
     publisher = {mathdoc},
     volume = {195},
     number = {6},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_6_a5/}
}
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A. S. Leonov. Functionals with the $H$-property in the Sobolev space~$W_1^1$. Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 879-896. http://geodesic.mathdoc.fr/item/SM_2004_195_6_a5/