Stability for semilinear elliptic variational inequalities depending on the gradient

In this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variational inequalities (Pn) with a nonlinear term depending on the gradient of the solution. This paper can be seen as the second part of the work Matzeu and Servadei (2010) [9], in the sense that here we give a stability result for the C1,α-weak solutions of problem (Pn) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (Pn), found with the arguments of Matzeu and Servadei (2010) [9], converge to a solution of the limiting problem (P), under suitable convergence assumptions on the data.