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The higher order regularity Dirichlet problem for elliptic systems in the upper-half space
Maria Martell, Jose Mitrea, Donna Mitrea, Irina Mitrea, Marius
Maria Martell, Jose
Mitrea, Donna
Mitrea, Irina
Mitrea, Marius
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2014
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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.
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American Mathematical Society
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HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS
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