THE DIRCHLET PROBLEM FOR A CERTAIN DEGENERATE ELLIPTIC EQUATION AND POTENTIAL METHOD

In this paper we consider the Dirichlet problem for the equation uxx+yuyy= 0 （y】0） on the domainDlocated in upper half-plane, which is bounded by the suitable smooth curve T with the ends A; （-α, 0）and B; （α, 0） and the segment AB. By means of the potential method, the uniqueness and existence of the so-lution of the problem,having a representation of potential, are proved.0 A Special Solution With An Logarithmic SingularityLet two points in upper half-plane, P; （x, y） and M; （ζ,η）, be given. We may construct a special so-lution of the equation above as follows;