Volume 29, 2023
|Number of page(s)||23|
|Published online||27 April 2023|
An inverse problem for a double phase implicit obstacle problem with multivalued terms
1 Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P.R. China
2 Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China
3 Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30-348 Kraków, Poland
4 School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China
5 Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland
6 Department of Mathematics, University of Craiova, Street A.I. Cuza 13, 200585 Craiova, Romania
7 Brno University of Technology, Faculty of Electrical Engineering and Communication, Technická 3058/10, Brno 61600, Czech Republic
8 Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Griviţei Street, 010702 Bucharest, Romania
9 Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
* Corresponding author: email@example.com
Accepted: 26 March 2023
In this paper, we study an inverse problem of estimating three discontinuous parameters in a double phase implicit obstacle problem with multivalued terms and mixed boundary conditions which is formulated by a regularized optimal control problem. Under very general assumptions, we introduce a multivalued function called a parameter-to-solution map which admits weakly compact values. Then, by employing the Aubin-Cellina convergence theorem and the theory of nonsmooth analysis, we prove that the parameter-to-solution map is bounded and continuous in the sense of Kuratowski. Finally, a generalized regularization framework for the inverse problem is developed and a new existence theorem is provided.
Mathematics Subject Classification: 35J20 / 35J25 / 35J60 / 35R30 / 49N45 / 65J20
Key words: Clarke subdifferential / discontinuous parameter / double phase operator / implicit obstacle problem / inverse problem / optimal control / Steklov eigenvalue problem
© The authors. Published by EDP Sciences, SMAI 2023
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