This article is cited in 3 papers

On the $H$-property of functionals in Sobolev spaces

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: 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.

UDC: 517.98

Received: 27.06.2002

DOI: 10.4213/mzm2500

 English version: Mathematical Notes, 2005, 77:3, 348–363

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