TY  - JOUR
ID  - Orpel2006
LB  - Orpel2006
AU  - Orpel, Aleksandra
TI  - Continuous dependence of solutions of elliptic BVPs on parameters
ST  - Continuous dependence of solutions of elliptic BVPs on parameters
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 351
EP  - 359
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.351
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.351
AB  - 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.
KW  - continuous dependence on parameters
KW  - elliptic Dirichlet problems
KW  - optimal control problem
SN  - 1232-9274
ER  -