Opuscula Math.
26
, 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.