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Continuous dependence of solutions of elliptic BVPs on parameters

Keywords: continuous dependence on parameters , elliptic Dirichlet problems , optimal control problem

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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 $\{x_k\}_{k\in N}$) 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.

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