On Estimates of Solutions to Boundary-Value Problems for Elliptic Systems in a Layer

General boundary-value problems for elliptic systems in a layer, i.e., in a domain of the form
$$ \Pi=\{(x',x_{n})\in \mathbb{R}^n\mid x'\in\mathbb{R}^{n-1},\,x_{n}\in (a,b)\}, \qquad -\infty<a<b<+\infty,\;n\ge3, $$
are considered under the Lopatinskii condition. Solvability theorems are proved, and estimates of solutions are obtained.