ON THE SMOOTHNESS OF SOLUTIONS OF DIFFERENTIAL EQUATIONS AT SINGULAR POINTS OF THE BOUNDARY OF THE DOMAIN

Second-order elliptic equations with analytic coefficients and right sides in a domain with piecewise smooth boundary are studied. It is assumed that the boundary is characteristic at all points. Both Lipschitz and non-Lipschitz singularities of the boundary are admitted. It is proved that for large values of the spectral parameter, solutions possess high smoothness even at those points where the boundary has singularities. The results are based on the study of a constructive representation of solutions of the equations in the form of series of analytic functions.