On a convex combination of solutions of elliptic variational inequalities

M. BOUKROUCHE – D.A. TARZIA

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

Texas Univ. (USA)

Lugar: Texas; Año: 2007 vol. 2007 p. 1 - 10

1072-6691

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.