Continuous dependence of solutions of elliptic BVPs on parameters - Aleksandra Orpel (Opuscula Mathematica, 2006)
The continuous dependence of solutions for a certain class of elliptic PDE on functional parameters is studied in this paper. The main result is as follow: the sequence \(\{x_k\}_{k\in N}\) of solutions of the Dirichlet problem discussed here (corresponding to parameters \(\{u_k\}_{k\in N}\)) converges weakly to \(x_0\) (corresponding to \(u_0\)) in \(W^{1,q}_0(Ω,R)\), provided that \(\{u_k\}_{k\in N}\) tends to \(u_0\) a.e. in \(Ω\). Our investigation covers both sub and superlinear cases. We apply this result to some optimal control problems.