On the solvability of a variational inequality problem and application to a problem of two membranes

A. Addou and E. B. Mermri

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-6

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 = ( u 1 , u 2 ) ∈ K such that for all v = ( v 1 , v 2 ) ∈ K , ∫ Ω ∇ u 1 ∇ ( v 1 − u 1 ) + ∫ Ω ∇ u 2 ∇ ( v 2 − u 2 ) + ( f , v − u ) ≥ 0 as a system of independent equations, where f belongs to L 2 ( Ω ) × L 2 ( Ω ) and K = { v ∈ H 0 1 ( Ω ) × H 0 1 ( Ω ) : v 1 ≥ v 2 a .e . in Ω } .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:738924

DOI: 10.1155/S0161171201004823

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