The Сauchy problem for a biharmonic equation of helmholtz type
0009-0002-8119-3037 The material was received by the Editorial Board: 03.04.2025
An explicit reconstruction formula is proposed for a 2-metaharmonic function in a domain from its known values, the values of its normal derivative, the values of its Laplacian, and the values of the normal derivative of its Laplacian on a part of the boundary. That is, an explicit continuation formula is obtained, as well as a regularization of the solution to the Cauchy problem for the given equation.
УДК 517.956+517.958:539.3
Keywords: Cauchy problem, metaharmonic equation, metaharmonic function, elliptic equations, ill-posed problem, Carleman function.
References: Makhmudov К.О., Makhmudov О.I., Niyozov I.Е. The Сauchy problem for a biharmonic equation of helmholtz type. Mat. Trudy. 2026, 29, № 2. P. 52–73. DOI: 10.25205/1560-750X-2026-29-2-52-73