Inverse problems for a class of elliptic obstacle problems involving multivalued convection term and weighted $(p, q)$-Laplacian. (2nd January 2023)

• Record Type: Journal Article
• Authors: Zeng, Shengda; Migórski, Stanisław; Khan, Akhtar A.; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 321
• Page End: 349
• Publication Date: 2023-01-02
• Subjects: Inverse problem -- multivalued convection -- regularization -- weighted (p, q)-Laplacian -- elliptic obstacle problem; 35R30 -- 49N45 -- 65J20 -- 35J20 -- 35J25 -- 35J60; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2088371
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we study the inverse problem of estimating discontinuous parameters and boundary data in a nonlinear elliptic obstacle problem involving a nonhomogeneous, nonlinear partial differential operator, which is given as a sum of a weighted p -Laplacian and a weighted q -Laplacian (called the weighted ( p, q ) -Laplacian), a multivalued convection term (a multivalued reaction term depending on the gradient), a multivalued boundary condition and an obstacle constraint. Under general hypotheses on the data, we prove the existence of a nontrivial solution to the elliptic obstacle problem, which depends on the first eigenvalue of the Steklov eigenvalue problem for the p -Laplacian. We also establish the boundedness and the closedness of the solution set to the problem. For the parameter-to-solution map, we give a convergence result of the Kuratowski type and prove the solvability of the inverse problem.