A Boundary Value Problem for a Mixed Type Equation in a Cylindrical Domain

We examine a boundary value problem for a mixed type equation of the second order in a cylindrical domain. Under certain conditions, the existence of regular solutions in a suitable weighted Sobolev space is proven by regularization. The uniqueness of solutions is also established under the same conditions. A few estimates of the second derivatives of a generalized solution are obtained in the elliptic-parabolic domain.

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