Geodesic
On Estimates of Solutions to Boundary-Value Problems for Elliptic Systems in a Layer
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 60-70

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General boundary-value problems for elliptic systems in a layer, i.e., in a domain of the form $$ \Pi=\{(x',x_{n})\in \mathbb{R}^n\mid x'\in\mathbb{R}^{n-1},\,x_{n}\in (a,b)\}, \qquad -\infty+\infty,\;n\ge3, $$ are considered under the Lopatinskii condition. Solvability theorems are proved, and estimates of solutions are obtained.
Keywords: layer, elliptic system, elliptic boundary-value problem. 
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     author = {V. A. Nikishkin},
     title = {On {Estimates} of {Solutions} to {Boundary-Value} {Problems} for {Elliptic} {Systems} in a {Layer}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {45},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a3/}
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V. A. Nikishkin. On Estimates of Solutions to Boundary-Value Problems for Elliptic Systems in a Layer. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 60-70. http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a3/