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    The higher order regularity Dirichlet problem for elliptic systems in the upper-half space

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    Date
    2014
    Author
    Maria Martell, Jose
    Mitrea, Donna
    Mitrea, Irina
    Mitrea, Marius
    Subject
    math.AP
    math.AP
    math.CA
    Primary: 35B65, 35J45, 35J57, Secondary: 35C15, 74B05, 74G05
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5902
    
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    DOI
    10.1090/conm/612/12228
    Abstract
    We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in $L^p$-based Sobolev spaces, $1<p<\infty$, of arbitrary smoothness $\ell$, is well-posed in the class of functions whose nontangential maximal operator of their derivatives up to, and including, order $\ell$ is $L^p$-integrable. This class includes all scalar, complex coefficient elliptic operators of second order, as well as the Lam\'e system of elasticity, among others.
    Citation to related work
    American Mathematical Society
    Has part
    HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5884
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