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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 6, 1983, pp. 523–551
DOI: 10.4171/ZAA/83

Published online: 1983-12-31

The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries. II (in Russian)

Vladimir G. Maz'ya[1] and Boris A. Plamenevskii[2]

(1) Linköping University, Sweden
(2) St. Petersburg State University, Russian Federation

This is a continuation of the author’s paper in ZAA 4 (1983) devoted to the Dirichiet problem for the linear Stokes system in a piece-vise smooth domain in $\mathbb R^3$. Here the estimates for the Green tensor and Miranda-Agmon maximum principle are proved. Similar results are obtained for Lamé’s equations. The existence of a strong solution of the Dirichlet problem for the Navier-Stokes equations is proved along with some estimates for this solution.

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Maz'ya Vladimir, Plamenevskii Boris: The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries. II (in Russian). Z. Anal. Anwend. 2 (1983), 523-551. doi: 10.4171/ZAA/83