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    • Graduate School - MU Theses and Dissertations (MU)
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    • 2005 Dissertations (MU)
    • 2005 MU dissertations - Freely available online
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    The poisson problem on Lipschitz domains

    Mayboroda, Svitlana
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    [PDF] research.pdf (1.141Mb)
    Date
    2005
    Format
    Thesis
    Metadata
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    Abstract
    The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces on arbitrary Lipschitz domains. The main theorems we prove extend the work of D. Jerison and C. Kenig [JFA, 95], whose methods and results are largely restricted to the case p_ 1, and answer the open problem #3.2.21 on p. 121 in C. Kenig's book in the most complete fashion. When specialized to Hardy spaces, our results provide a solution of a (strengthened form of a) conjecture made by D.-C. Chang, S.Krantz and E. Stein regarding the regularity of the Green potentials on Hardy spaces in Lipschitz domains. The corollaries of our main results include new proofs and various extensions of: Hardy space estimates for Green potentials in convex domains due to V. Adolfsson, B.Dahlberg, S. Fromm, D. Jerison, G.Verchota and T.Wolff and the Lp - Lq estimates for the gradients of Green potentials in Lipschitz domains, due to B. Dahlberg.
    URI
    http://hdl.handle.net/10355/4133
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Collections
    • 2005 MU dissertations - Freely available online
    • Mathematics electronic theses and dissertations (MU)

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