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arXiv · 1405.2999

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

José María Martell·Dorina Mitrea·Irina Mitrea·Marius Mitrea
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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 Lamé system of elasticity, among others.

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José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea. 2014-05-12. The higher order regularity Dirichlet problem for elliptic systems in the upper-half space. https://doi.org/10.1090/conm%2F612%2F12228

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