@Article{Orpel2006,
author = "Orpel, Aleksandra",
title = "Continuous dependence of solutions of elliptic BVPs on parameters",
journal = "Opuscula Math.",
year = "2006",
volume = "26",
number = "2",
pages = "351--359",
doi = "http://dx.doi.org/10.7494/OpMath.2006.26.2.351",
url = "http://dx.doi.org/10.7494/OpMath.2006.26.2.351",
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",
issn = "1232-9274"
}