%0 Journal Article
%T Continuous dependence of solutions of elliptic BVPs on parameters
%A Aleksandra Orpel
%J Opuscula Mathematica
%D 2006
%I AGH University of Science and Technology
%X 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 $\{x_k\}_{k\in N}$) converges weakly to $x_0$ (corresponding to $u_0$) in $W^{1,q}_0(\Omega,R)$, provided that $\{x_k\}_{k\in N}$ 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.
%K continuous dependence on parameters
%K elliptic Dirichlet problems
%K optimal control problem
%U http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2625.pdf