Abstract:

In this paper, we obtain interior Holder continuity for solutions of the fourth-order elliptic system

Delta(2)u = Delta(V center dot del u) + div(w del u) + W center dot del u

formulated by Lamm and Riviere [Comm. Partial Differential Equations 33 (2008) 245-262]. Boundary continuity is also obtained under a standard Dirichlet or Navier boundary condition. We also use conservation law to establish a weak compactness result which generalizes a result of Riviere for the second-order problem.

(Link: https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12289)

Papers Published：
[1] C.-Y. Guo and C.-L. Xiang, Regularity of solutions for a fourth-order elliptic system via conservation law. J. Lond. Math. Soc. (2) 101 (2020), no. 3, 907-922.
[2] C.-Y. Guo, C.-L. Xiang and G.-F. Zheng, The Lamm-Riviere system I: Lp regularity theory, Cal. Var. PDEs 60 (2021), no. 6, Paper No. 213.
[3] C.-Y. Guo and C.-L. Xiang, Regularity of weak solutions to higher order elliptic systems in critical dimensions. Tran. Amer. Math. Soc. 374 (2021), no. 5, 3579-3602

Prof. Guo Changyu (Shandong University)