Singular solutions to Protter problem for Keldysh type equations

Abstract

Three-dimensional boundary value problem for equations of Keldysh type is studied. It is known that this problem is not well-posed, since it has infinite-dimensional co-kernel. In the present paper it is shown that for n ∈ N there exist a smooth right-hand side function fn, for which the corresponding unique generalized solution has a strong power-type singularity. This singularity is isolated at the vertex O of the inner characteristic surface and does not propagate along the surface. As well as, an exact a priory estimate for unique generalized solution is stated.