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.