The first boundary value problem for classical equations of mathematical physics in domains with piecewise-smooth boundaries. I (in Russian)
Vladimir Gilelevich Maz'ya, Boris Alekseevich Plamenevskii · Zeitschrift für Analysis und ihre Anwendungen · 1983
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.