Carleman’s formula of a solutions of the Poisson equation in bounded domain. (English) Zbl 1486.35155

Summary: We suggest an explicit continuation formula for a solution to the Cauchy problem for the Poisson equation in a domain from its values and values of its normal derivative on a part of the boundary. We construct the continuation formula of this problem based on the Carleman-Yarmuhamedov function method.


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
Full Text: DOI MNR


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