José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea
Published 2014-05-12Version 1
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.
Journal: Harmonic Analysis and Partial Differential Equations. Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 11-15, 2012, Contemporary Mathematics 612 (2014), 123-141
The BMO-Dirichlet problem for elliptic systems in the upper-half space and quantitative characterizations of VMO
The $p$-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenisation problems
The $L^p$ Dirichlet and Regularity problems for second order Elliptic Systems with application to the Lamé system
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