International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 9, Pages 603-608
doi:10.1155/S0161171201004823
On the solvability of a variational inequality problem and application to a problem of two membranes
University Mohamed I, Faculty of Sciences, Department of Mathematics and Computer Sciences, Oujda, Morocco
Received 17 March 2000
Copyright © 2001 A. Addou and E. B. Mermri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The purpose of this work is to give a continuous convex function,
for which we can characterize the subdifferential, in order to
reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2 a.e. in Ω}.