New preprint on non-coercive Neumann boundary control problems

21 March 2024

The manuscript deals with the discretization of an optimal control problem for a non-coercive boundary value problem. The motivation was to require as few assumptions as possible in order to better capture their meaning: The domain needs not be convex, the data should be as non-regular as possible and coercivity of the differential operator is not required. In particular, the lack of coercivity means that standard techniques such as the use of the Lax-Milgram lemma or Céa's lemma are not practicable. Nevertheless, it has been possible not only to reproduce the known estimates of the discretization error, which have been proven under much stronger conditions, but also to improve one result.

Thomas Apel, Mariano Mateos und Arnd Rösch: Non-coercive boundary control problems. Preprint.