Optimal control of fractional elliptic PDEs with state constraints and characterization of the dual of fractional-order Sobolev spaces

DOI10.1007/s10957-020-01684-zzbMath1443.49005arXiv1906.00032OpenAlexW3027467862MaRDI QIDQ779847

Harbir Antil, Mahamadi Warma, Deepanshu Verma

Publication date: 14 July 2020

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.00032

zbMATH Keywords

state and control constraintsfractional Laplaciancharacterization of fractional dual spacesmeasure valued dataoptimal control with PDE constraintregularity of optimal controlregularity of solutions to state and adjoint equations

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical methods for integral equations (65R20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary value problems for PDEs with pseudodifferential operators (35S15) Existence theories for optimal control problems involving partial differential equations (49J20) Fractional partial differential equations (35R11)

Related Items (10)

Finite element approximation of time fractional optimal control problem with integral state constraint ⋮ Optimal control of a nonlinear PDE governed by fractional Laplacian ⋮ Inverse source problem for Sobolev equation with fractional Laplacian ⋮ A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator Equations ⋮ An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint ⋮ On the optimal control of a linear peridynamics model ⋮ Error estimates for fractional semilinear optimal control on Lipschitz polytopes ⋮ Computational inverse problems for partial differential equations. Abstracts from the workshop held December 6--12, 2020 (hybrid meeting) ⋮ On a Fractional Version of a Murat Compactness Result and Applications ⋮ Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data

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