More on a Boundary Value Problem with Polynomials

An approximation in Sobolev classes is obtained to the solution of a general boundary value problem for a self-adjoint elliptic operator of order $2l$ with constant coefficients on an $n$-dimensional ellipsoid. The right-hand side of the equation is a function from the class $W_2^r$, and the boundary conditions are homogeneous. The approximation is obtained by algebraic polynomials that are solutions to the boundary value problem for the same differential operator.