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.
| Mualliflar | А. Б. Хасанов, U. Yu. Juraeva |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashr sanasi | 2025-03-29 |
| Jild | 1 |
| Son | 1 |
| Betlar | 93-101 |
| Til | en |
| DOI | 10.59251/2181-1296.2025.v1.149.2.3394 |
DOI: 10.59251/2181-1296.2025.v1.149.2.3394 · Maqolaning asl sahifasi
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