Fatou-type theorems and boundary value problems for elliptic systems in the upper half-space

Martell, J.; Mitrea, D.; Mitrea, I.; Mitrea, M.

doi:10.1090/spmj/1592

Fatou-type theorems and boundary value problems for elliptic systems in the upper half-space
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by J. M. Martell, D. Mitrea, I. Mitrea and M. Mitrea

St. Petersburg Math. J. 31 (2020), 189-222

DOI: https://doi.org/10.1090/spmj/1592

Published electronically: February 4, 2020

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Abstract:

This is a survey of recent progress in a program which to date has produced several publications and is aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb {R}}^n_+$ for second-order, homogeneous, constant complex coefficient, elliptic systems $L$, formulated in a manner that emphasizes pointwise nontangential boundary traces of the null-solutions of $L$ in ${\mathbb {R}}^n_+$.

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