期刊
ADVANCES IN NONLINEAR ANALYSIS
卷 12, 期 1, 页码 1-22出版社
DE GRUYTER POLAND SP Z O O
DOI: 10.1515/anona-2022-0223
关键词
discontinuous parameter; double phase operator; elliptic obstacle problem; inverse problem; mixed boundary condition; multivalued convection; Steklov eigenvalue problem
This article investigates the inverse problem of identifying a discontinuous parameter and a discontinuous boundary datum in an elliptic inclusion problem involving a double phase differential operator. By applying a surjectivity theorem for multivalued mappings and introducing the parameter-to-solution-map, the existence of nontrivial solutions and solvability of the inverse problem are examined and established.
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 p-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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