CARLEMAN'S FORMULA OF A SOLUTIONS OF THE POISSON EQUATION IN BOUNDED DOMAIN

Ermamat N. Sattorov     (Samarkand State University, Samarkand boulevard 15, Samarkand, Uzbekistan)
Zuxro E. Ermamatova     (Samarkand State University, Samarkand boulevard 15, Samarkand, Uzbekistan)

Abstract


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.


Keywords


Poisson equations, Ill-posed problem, Regular solution, Carleman--Yarmuhamedov function, Green's formula, Carleman formula, Mittag-Leffler entire function.

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References


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DOI: http://dx.doi.org/10.15826/umj.2021.2.008

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