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

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

Algebra i analiz, Tome 31 (2019) no. 2, pp. 3-50.

Résumé

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 ${\mathbb{R}}^n_{+}$.

Détail

Keywords: Fatou-type theorem, Dirichlet boundary value problem, elliptic system, Poisson kernel, nontangential maximal operator, nontangential boundary trace, Muckenhoupt weights, Hardy space, bounded mean oscillations, vanishing mean oscillations, subcritical growth, sublinear growth.

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