English

Second-order conditions for bang-bang control of elliptic equations in arbitrary dimensions

Optimization and Control 2026-02-17 v1

Abstract

We consider an optimal control problem governed by a semilinear PDE in cases where the optimal control is of bang-bang type. By utilizing the theory of Bessel potential space, we characterize quadratic growth of the objective via a second-order optimality condition. In contrast to previous contributions, our method of proof works in arbitrary spatial dimensions.

Keywords

Cite

@article{arxiv.2602.14632,
  title  = {Second-order conditions for bang-bang control of elliptic equations in arbitrary dimensions},
  author = {Gerd Wachsmuth},
  journal= {arXiv preprint arXiv:2602.14632},
  year   = {2026}
}