Identification of discontinuous parameters in double phase obstacle problems

Autor: Zeng Shengda, Bai Yunru, Winkert Patrick, Yao Jen-Chih
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Advances in Nonlinear Analysis, Vol 12, Iss 1, Pp 1-22 (2022)
Druh dokumentu: article
ISSN: 2191-950X
DOI: 10.1515/anona-2022-0223
Popis: In this article, we investigate the inverse problem of identification of a discontinuous parameter and a discontinuous boundary datum to an elliptic inclusion problem involving a double phase differential operator, a multivalued convection term (a multivalued reaction term depending on the gradient), a multivalued boundary condition and an obstacle constraint. First, we apply a surjectivity theorem for multivalued mappings, which is formulated by the sum of a maximal monotone multivalued operator and a multivalued pseudomonotone mapping to examine the existence of a nontrivial solution to the double phase obstacle problem, which exactly relies on the first eigenvalue of the Steklov eigenvalue problem for the pp-Laplacian. Then, a nonlinear inverse problem driven by the double phase obstacle equation is considered. Finally, by introducing the parameter-to-solution-map, we establish a continuous result of Kuratowski type and prove the solvability of the inverse problem.
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