# Convergence analysis for double phase obstacle problems with multivalued convection term

## Inst. Mathematik

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.