Abstract
In this paper we study an optimal control problem for a linear boundary value problem with strongly degenerate coefficient in the main part of the elliptic operator and with the Neumann boundary control. Given a cost functional, the objective is to provide the well-posedness analysis of the corresponding optimal control problem, prove existence of the optimal solutions and propose the scheme for their approximation.
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Durante, T., Kupenko, O.P. & Manzo, R. On optimal boundary control problem for a strongly degenerate elliptic equation. Rev Mat Complut 33, 63–88 (2020). https://doi.org/10.1007/s13163-019-00310-5
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DOI: https://doi.org/10.1007/s13163-019-00310-5
Keywords
- Strongly degenerate elliptic equation
- Boundary control
- Hardy–Poincarè inequality
- Weighted Sobolev spaces
- Attainability problem