Stability for semilinear elliptic variational inequalities depending on the gradient

Abstract

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 ( P n ) 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 C 1 , α -weak solutions of problem ( P n ) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of ( P n ) , 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.