Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 31, pp. 1-10.
Title: On a convex combination of solutions to elliptic variational
inequalities
Authors: Mahdi Boukrouche (Univ. of Saint-Etienne, France)
Domingo A. Tarzia (Univ. Austral, Rosario, Argentina)
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.