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Convergence analysis for double phase obstacle problems with multivalued convection term

Zeng, Shengda; Bai, Yunru; Gasiński, Leszek; Winkert, Patrick

In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term. Denoting by š“¢ the solution set of the obstacle problem and by š“¢n the solution sets of approximating problems, we prove the following convergence relation āˆ…ā‰ w-lim sup Sn (nā†’āˆž) =s-lim sup (nā†’āˆž) Sn āŠ‚ S, where w-lim supnā†’āˆž š“¢n and s-lim supnā†’āˆž š“¢n denote the weak and the strong Kuratowski upper limit of š“¢n, respectively.
Published in: Advances in Nonlinear Analysis, 10.1515/anona-2020-0155, De Gruyter