This article is cited in 2 papers

Functionals with the $H$-property in the Sobolev space $W_1^1$

A. S. Leonov

Moscow Engineering Physics Institute (State University)

Abstract: 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 $W_1^1$.

UDC: 517.98

MSC: 36E35

Received: 24.06.2003

DOI: 10.4213/sm829

 English version: Sbornik: Mathematics, 2004, 195:6, 879–896

Bibliographic databases:

• 
• 
• 
•