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

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Abstract

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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Correspondence to A. N. Artyushin.

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The author was supported by the Russian Foundation for Basic Research (Grant 18-51-41009).

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Artyushin, A.N. A Boundary Value Problem for a Mixed Type Equation in a Cylindrical Domain. Sib Math J 60, 209–222 (2019). https://doi.org/10.1134/S0037446619020034

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  • DOI: https://doi.org/10.1134/S0037446619020034

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