On a boundary control approach to domain embedding methods (Q2753212)

In order to solve some boundary value problems associated with a linear elliptic PDE with regular coefficients in a ``complicated'' domain \(\omega\), the authors propose to solve an optimal boundary control problem in a simple domain \(\Omega\) containing \(\omega\). When the controls are taken in a finite-dimensional subspace, they prove, using a controllability result due to J. L. Lions, that the solutions of the boundary value problem can be approximated by the solutions of the optimal control problem. The results are obtained for interior and exterior problems. Some numerical experiments are presented.