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

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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.

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Authors and Affiliations

  1. University of Minnesota, Minneapolis, MN, 55455, USA

    I. Mitrea

  2. University of Missouri, Columbia, MO, 65211, USA

    M. Mitrea

  3. Missouri State University, Springfield, MO, 65897, USA

    M. Wright

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  1. I. Mitrea
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Translated from Problems in Mathematical Analysis 51, November 2010, pp. 21–114

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Mitrea, I., Mitrea, M. & Wright, M. Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains. J Math Sci 172, 24–134 (2011). https://doi.org/10.1007/s10958-010-0187-4

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