Stability of Monotone Variational Inequalities with Various Applications

The convergence and stability theory of Mosco is extended by the more general approach of monotone - convex functionals and by weakening uniform equimonotonicity and equicoervity assumptions to semicoervity conditions. The abstract theory is firstly applied to a finite dimensional Variational Inequality that models distributed market equilibria with box constraints providing a stability result with respect to the upper bounds. Then it is applied to obtain stability results with respect to coefficients and unilateral constraints in p-harmonic elliptic unilateral boundary value problems that can be considered as scalar models of the unilateral contact problem without, respectively with given friction.

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