SOLUTION OF A BOUNDARY PROBLEM FOR AN ELLIPTIC EQUATION WITH A SMALL NONINTEGER ORDER DEGENERACY

We consider a Dirichlet boundary problem for an elliptic type equation with a non-regular degeneracy of noninteger order in a rectangle. The coefficients of the differential operator are supposed to be analytic. We build a formal solution by using the method for spectral separation of the singularities. The solution is series where its non-analytic dependency on ???? near point ???? = 0 is written explicitly. We proof the convergence of the series to the classical solution using the Green’s function method.