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arXiv · 2602.14632

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

Gerd Wachsmuth
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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.

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Gerd Wachsmuth. 2026-02-16. Second-order conditions for bang-bang control of elliptic equations in arbitrary dimensions. https://arxiv.org/abs/2602.14632

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