Zeng, ShengdaBai, YunruWinkert, PatrickYao, Jen-Chih2022-09-192022-09-192022-08-192191-9496https://depositonce.tu-berlin.de/handle/11303/17352http://dx.doi.org/10.14279/depositonce-16133In 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.en510 Mathematikdiscontinuous parameterdouble phase operatorelliptic obstacle probleminverse problemmixed boundary conditionmultivalued convectionSteklov eigenvalue problemArticle2191-950X