Integral Representation for Polyharmonic Functions in Two Dimensional Euclidean Space
Year: 2025
Type: article
Abstract: In this paper we consider the Cauchy problem for the n-order polyharmonic equation in an unbounded domain D, where boundary data are given on a part of boundary. The goal is to reconstruct a polyharmonic function u(y) in D based on the given values of u, its Laplacians, and their normal derivatives. This is the ill-posed problem, hence we use Carleman-type integral representations and stability estimates to ensure well-posed approximations. We construct the Carleman function and prove key inequalities governing its behavior.
Authors: A. Khasanov, U. Juraeva
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409648382