Convergence analysis for double phase obstacle problems with multivalued convection term

Advances in Nonlinear Analysis

article

Shengda Zeng¹  Yunru Bai²  Leszek Gasiński³  Patrick Winkert⁴ 

[1] Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University;Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science;Pedagogical University of Cracow, Department of Mathematics;Technische Universität Berlin, Institut für Mathematik

关键词: Double phase problem;    multivalued convection term;    Kuratowski upper limit;    Tychonov fixed point principle;    obstacle problem;   

DOI  :  10.1515/anona-2020-0155

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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 ? the solution set of the obstacle problem and by ? n the solution sets of approximating problems, we prove the following convergence relation ∅ ≠ w-lim supn→ ∞ Sn=s-lim supn→ ∞ Sn⊂ S, $$\begin{array}{} \displaystyle \emptyset\neq w\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n=s\text{-}\limsup\limits_{n\to\infty}{\mathcal S}_n\subset \mathcal S, \end{array}$$ where w -lim sup n →∞ ? n and s -lim sup n →∞ ? n denote the weak and the strong Kuratowski upper limit of ? n , respectively.

【 授权许可】

CC BY