On the asymptotic behaviour of solutions of integro-differential inequalities (Q1122096)

The authors study the limiting behaviour of solutions \(u_{\lambda}\) of the unilateral problem \[ (1)\quad (Au_{\lambda}+\lambda u_{\lambda}- f)\vee (u_{\lambda}-\psi)=0\quad in\quad \Omega,\quad Bu_{\lambda}=0\quad on\quad \partial \Omega \] as the positive parameter \(\lambda\) tends to zero. Here \(\vee\) denotes the maximum between real numbers, A is an elliptic integro-differential operator of second order and B is a differential operator of first order. The main tool employed to establish the results is based on precise estimates of the Green function for the initial-boundary value problem associated with A and B.