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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Gerd Wachsmuth
DOI: 10.48550/arxiv.2602.14632
Cited by: 0

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.

Fields of Study & Subjects

Stability and Controllability of Differential Equations Nonlinear Partial Differential Equations Advanced Numerical Methods in Computational Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
16 February 2026
Language
EN
Document type
Preprint