Geodesic
On the $H$-property of functionals in Sobolev spaces
Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 378-394

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In this paper, we consider special classes of strongly convex functionals in Sobolev spaces. It is proved that functionals from such classes have the so-called $H$-property: weak convergence of sequences of arguments and convergence of such sequences with respect to a given functional imply strong convergence. 
@article{MZM_2005_77_3_a5,
     author = {A. S. Leonov},
     title = {On the $H$-property of functionals in {Sobolev} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {378--394},
     publisher = {mathdoc},
     volume = {77},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a5/}
}
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A. S. Leonov. On the $H$-property of functionals in Sobolev spaces. Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 378-394. http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a5/