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Journal of Mathematical Sciences

, Volume 172, Issue 1, pp 24–134 | Cite as

Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains

  • I. MitreaEmail author
  • M. Mitrea
  • M. Wright
Article

We establish the well-posedness of the inhomogeneous Dirichlet problem for Δ2 in arbitrary Lipschitz domains in \( {\mathbb{R}^3} \), with data from Besov–Triebel–Lizorkin spaces, for the optimal range of indices. The main novel contribution is to allow for certain nonlocally convex spaces to be considered, and to establish integral representations for the solution. Bibliography: 57 titles. Illustrations: 1 figure.

Keywords

Hardy Space Besov Space Lipschitz Domain Singular Integral Operator Biharmonic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.University of MinnesotaMinneapolisUSA
  2. 2.University of MissouriColumbiaUSA
  3. 3.Missouri State UniversitySpringfieldUSA

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