Opuscula Math. 26, no. 2 (2006), 351-359
Opuscula Mathematica
Continuous dependence of solutions of elliptic BVPs on parameters
Abstract. 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 \(W^{1,q}_0(\Omega,R)\), provided that \(\{u_k\}_{k\in N}\) tends to \(u_0\) a.e. in \(\Omega\). Our investigation covers both sub and superlinear cases. We apply this result to some optimal control problems.
Keywords: continuous dependence on parameters, elliptic Dirichlet problems, optimal control problem.
Mathematics Subject Classification: 49K40, 49K20, 35J20, 35J60.
- Aleksandra Orpel
- University of Łódź, Faculty of Mathematics, ul. Banacha 22, 90-238 Łódź, Poland
- Received: 2005-09-09.
