An a priori estimate for the norms of solutions of the Dirichlet problem for a class of regular operators (Q5930597)

The author regards a priori estimates for the solutions of the Dirichlet problem of a class of differential operators with constant coefficients on polyhedra. The work is rather technical. For the class of polyhedra, called completely proper, different polynomial functions appointed by vertices of the polyhedron are regarded. Using these functions the author defines spaces of fractional Sobolev type and Besov type, as well as regularity of the regarded differential operators. The a priori estimates for the solutions of the Dirichlet problem are formulated for the above operators in terms of norms of the above function spaces. A special class of pyramid-like polyhedra and regular pyramid-like operators is also regarded.