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arXiv · 2304.13853

Optimal control of a class of semilinear fractional elliptic equations

Cyrille Kenne·Gisèle Mophou·Mahamadi Warma
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Abstract

In this paper, a class of semilinear fractional elliptic equations associated to the spectral fractional Dirichlet Laplace operator is considered. We establish the existence of optimal solutions as well as a minimum principle of Pontryagin type and the first order necessary optimality conditions of associated optimal control problems. Second order conditions for optimality are also obtained for $L^{\infty}$ and $L^2-$ local solutions under some structural assumptions.

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Cyrille Kenne, Gisèle Mophou, Mahamadi Warma. 2023-04-26. Optimal control of a class of semilinear fractional elliptic equations. https://arxiv.org/abs/2304.13853

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