On a convex combination of solutions to elliptic variational inequalities

Abstract

Let ugi the unique solutions of an elliptic variational inequality with second member gi (i = 1, 2). We establish necessary and sufficient conditions for the convex combination tug1 + (1 - t)ug2, to be equal to the unique solution of the same elliptic variational inequality with second member tg1 + (1 - t)g2. We also give some examples where this property is valid.