On a Dirichlet Problem for Properly Elliptic Equation in the Space of Continuous Functions

The Dirichlet problem for $$2N$$ order properly elliptic equation with constant coefficients in the unit disc is considered. We seek the solution of the problem in the class of functions $$2N$$ times continuously differentiable in the disc and continuous up to the boundary with the derivatives of order not more than $$N-1$$ . The necessary and sufficient conditions for solvability of this problem are obtained and if these conditions hold the solution is determined in explicit form.