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    A priori estimates for solutions of elliptic partial differential equations on surfaces

    Steenblock, Heidi, 1984-
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    Date
    2009
    Format
    Thesis
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    Abstract
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let S be an ([lowercase nu ? 1)-dimensional bounded surface of class C[superscript 2] in [double-struck R][superscript n] and let [uppercase delta]S be the Laplace-Beltrami operator on S. In this thesis, under suitable geometric assumptions, we prove a priori estimates in the W[superscript 2,2] (S) Sobolev space for solutions u to the Poisson problem [uppercase delta][subscript S]u = f in S and u satisfying homogeneous Dirichlet, Neumann, or mixed type boundary conditions, in terms of the L[superscript 2] norm of the datum f. The geometric assumptions S has to satisfy are related to the mean curvatures of the boundary of the surface S.
    URI
    https://doi.org/10.32469/10355/10133
    https://hdl.handle.net/10355/10133
    Degree
    M.S.
    Thesis Department
    Mathematics (MU)
    Rights
    Access is limited to the campus of the University of Missouri--Columbia.
    Collections
    • 2009 MU theses - Access restricted to MU
    • Mathematics electronic theses and dissertations (MU)

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