The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1706 KB) | Metadata | Table of Contents | ZAA summary
Volume 2, Issue 4, 1983, pp. 335–359
DOI: 10.4171/ZAA/71

Published online: 1983-08-31

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

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

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

The first boundary value problem for the Stokes, Navier-Stokes, Lamé sytems and for the Laplace equation in a bounded domain $\Omega \subset \mathbb R^3$ is studied. The boundary of $\Omega$ contains singularities, such as conic points, edges or polyhedral angles. Theorems on solvability in spaces, supplied with weighted $L_s-$ and $C^{\alpha}-$ norms ($1 < s < \infty, 0 < \alpha < 1$) are proved. Coercive estimates of solutions in these spaces as well as pointwise estimates of the Green functions are obtained. The change of properties of generalized solutions under the change of right-hand sides is observed.

No keywords available for this article.

Maz'ya Vladimir, Plamenevskii Boris: The first boundary value problem for classical equations of mathematical physics in domains with piecewise-smooth boundaries. I (in Russian). Z. Anal. Anwend. 2 (1983), 335-359. doi: 10.4171/ZAA/71