Zeitschrift für Analysis und ihre Anwendungen
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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 and Boris A. Plamenevskii (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