×

zbMATH — the first resource for mathematics

A Carleman function and the Cauchy problem for the Laplace equation. (Russian, English) Zbl 1051.31002
Sib. Mat. Zh. 45, No. 3, 702-719 (2004); translation in Sib. Math. J. 45, No. 3, 580-595 (2004).
The author suggests an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., he gives an explicit continuation formula and a regularization procedure for a solution to the Cauchy problem for the Laplace equation.

MSC:
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDF BibTeX XML Cite
Full Text: EMIS EuDML