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- W4225968051 abstract "In this paper, we derive explicit second-order necessary and sufficient optimality conditions of a local minimizer to an optimal control problem for a quasilinear second-order partial differential equation with a piecewise smooth but not differentiable nonlinearity in the leading term. The key argument rests on the analysis of level sets of the state. Specifically, we show that if a function vanishes on the boundary and its the gradient is different from zero on a level set, then this set decomposes into finitely many closed simple curves. Moreover, the level sets depend continuously on the functions defining these sets. We also prove the continuity of the integrals on the level sets. In particular, Green's first identity is shown to be applicable on an open set determined by two functions with nonvanishing gradients. In the second part to this paper, the explicit sufficient second-order conditions will be used to derive error estimates for a finite-element discretization of the control problem." @default.
- W4225968051 created "2022-05-05" @default.
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- W4225968051 date "2022-03-31" @default.
- W4225968051 modified "2023-09-27" @default.
- W4225968051 title "Numerical analysis of a nonsmooth quasilinear elliptic control problem: I. Explicit second-order optimality conditions" @default.
- W4225968051 doi "https://doi.org/10.48550/arxiv.2203.16865" @default.
- W4225968051 hasPublicationYear "2022" @default.
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