Electron. J. Diff. Eqns., Vol. 2007(2007), No. 31, pp. 1-10.

On a convex combination of solutions to elliptic variational inequalities

Mahdi Boukrouche, Domingo A. Tarzia

Abstract:
Let $u_{g_i}$ the unique solutions of an elliptic variational inequality with second member $g_i$ ($i=1,2$). We establish necessary and sufficient conditions for the convex combination $t u_{g_1}+ (1-t) u_{g_2}$, to be equal to the unique solution of the same elliptic variational inequality with second member $t g_1+ (1-t) g_2$. We also give some examples where this property is valid.

Submitted September 15, 2006. Published February 22, 2007.
Math Subject Classifications: 35R35.
Key Words: Elliptic variational inequalities; convex combination of its solutions.

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Mahdi Boukrouche
Laboratory of Mathematics, University of Saint-Etienne
23 rue du Dr Paul Michelon
Saint-Etienne, 42023, France
Phone: 33 4 77 48 15 35; fax: 33 4 77 25 60 71
email: Mahdi.Boukrouche@univ-st-etienne.fr
Domingo A. Tarzia
Departamento Matemática - CONICET
FCE, Univ. Austral
Paraguay 1950, S2000FZF Rosario, Argentina
email: Domingo.Tarzia@fce.austral.edu.ar

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