On a generalization of the Keldysh theorem
George Jaiani · Georgian Mathematical Journal · 1995
Abstract. The Keldysh theorem for an elliptic equation with characteristic parabolic degeneration is generalized for the case of an elliptic equation of the second-order canonical form with order and type degeneration. The criteria under which the Dirichlet or Keldysh problems are correct are given in a one-sided neighborhood of the degeneration segment, enabling one to write the criteria in a single form. Moreover, some cases are pointed out in which it is even nessesary to give a criterion in the neighborhood because it is impossible to establish it on the segment of degeneracy of the equation. Let us consider the equation L(u) def = y m ∂2 u ∂x2 + yn ∂2u + a(x, y)∂u