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

Abstract

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.