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🆕 Date Issued:
2020-11-26
🗄 In DepositOnce:2021-01-06
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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 𝓢 the solution set of the obstacle problem and by 𝓢n the solution sets of approximating problems, we prove the following convergence relation ∅≠w-lim sup Sn (n→∞) =s-lim sup (n→∞) Sn ⊂ S, where w-lim supn→∞ 𝓢n and s-lim supn→∞ 𝓢n denote the weak and the strong Kuratowski upper limit of 𝓢n, respectively.
double phase problemmultivalued convection termKuratowski upper limitTychonov fixed point principleobstacle problem35J2035J2535J60
Published in: Advances in Nonlinear Analysis, 10.1515/anona-2020-0155, De Gruyter
Creative Commons Attribution 4.0 (CC BY)Creative Commons Attribution 4.0 (CC BY)
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