On a convex combination of solutions to elliptic variational inequalities

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.

Keywords

• Elliptic variational inequalities
• convex combination of its solutions.