Convergence analysis for double phase obstacle problems with multivalued convection term
Shengda Zeng, Yunru Bai, Leszek Gasiński, Patrick Winkert · Advances in Nonlinear Analysis · 2020
Abstract 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 𝓢 n the solution sets of approximating problems, we prove the following convergence relation ∅ ≠ w - lim sup n → ∞ S n = s - lim sup n → ∞ S n ⊂ S , $$\begin{array}{} \displaystyle \emptyset eq w\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n=s\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n\subset \mathcal S, \end{array}$$ where w -lim sup n →∞ 𝓢 n and s -lim sup n →∞ 𝓢 n denote the weak and the strong Kuratowski upper limit of 𝓢 n , respectively.