# On the Cauchy problem for the Helmholtz equation

## Keywords:

Integral formula, Matrix factorization, Helmholtz equation, Bounded domain, Cauchy problem## Abstract

The work is devoted to the study of continuation and evaluation of the stability of the solution of the Cauchy problem for the Laplace equation in a domain from its known values on the smooth part of the boundary of the domain. The problem under consideration belongs to the problems of mathematical physics, in which there is no continuous dependence of solutions on the initial data. When solving applied problems, it is necessary to find not only an approximate solution, but also a derivative of the approximate solution.

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