Opuscula Mathematica

Opuscula Math.
, no. 2
 (), 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.
Cite this article as:
Aleksandra Orpel, Continuous dependence of solutions of elliptic BVPs on parameters, Opuscula Math. 26, no. 2 (2006), 351-359
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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