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Regularity of solutions for a fourth‐order elliptic system via Conservation law
Author(s) -
Guo ChangYu,
Xiang ChangLin
Publication year - 2020
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12289
Subject(s) - conservation law , order (exchange) , mathematics , compact space , boundary (topology) , partial differential equation , mathematical analysis , dirichlet boundary condition , boundary value problem , dirichlet problem , dirichlet distribution , law , pure mathematics , political science , economics , finance
In this paper, we obtain interior Hölder continuity for solutions of the fourth‐order elliptic systemΔ 2 u = Δ ( V · ∇ u ) + div ( w ∇ u ) + W · ∇ u formulated by Lamm and Rivière [ 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 Rivière for the second‐order problem.