Geodesic
On a convex combination of solutions to elliptic variational inequalities
Electronic journal of differential equations, Tome 2007 (2007)
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.
Classification : 35R35
Keywords: elliptic variational inequalities, convex combination of its solutions 
@article{EJDE_2007__2007__a145,
     author = {Boukrouche,  Mahdi and Tarzia,  Domingo A.},
     title = {On a convex combination of solutions to elliptic variational inequalities},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1115.35155},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a145/}
}
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AU  - Tarzia,  Domingo A.
TI  - On a convex combination of solutions to elliptic variational inequalities
JO  - Electronic journal of differential equations
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VL  - 2007
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%A Tarzia,  Domingo A.
%T On a convex combination of solutions to elliptic variational inequalities
%J Electronic journal of differential equations
%D 2007
%V 2007
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%F EJDE_2007__2007__a145
Boukrouche,  Mahdi; Tarzia,  Domingo A. On a convex combination of solutions to elliptic variational inequalities. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a145/