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 |
| Nashriyot | Самарқанд давлат университети |
| ISSN | 2091-5446, 2181-1296 |
| Nashr sanasi | 2025-03-29 |
| Jild | 1 |
| Son | 1 |
| Betlar | 93-101 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.59251/2181-1296.2025.v1.149.2.3394 |
| Indeksga qo‘shilgan | 2026-09-02 |
DOI: 10.59251/2181-1296.2025.v1.149.2.3394 · Maqolaning asl sahifasi
| APA | А. Б. Хасанов, & U. Yu. Juraeva (2025). INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(1), 93-101. https://doi.org/10.59251/2181-1296.2025.v1.149.2.3394 |
|---|---|
| GOST (OAK) | А. Б. Хасанов, U. Yu. Juraeva INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2025. – T. 1, № 1. – P. 93-101. – DOI: 10.59251/2181-1296.2025.v1.149.2.3394. |
| MLA | А. Б. Хасанов, and U. Yu. Juraeva. “INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(1), 93-101, 2025. https://doi.org/10.59251/2181-1296.2025.v1.149.2.3394 |
| Chicago | А. Б. Хасанов, and U. Yu. Juraeva. “INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(1), 93-101 (2025). https://doi.org/10.59251/2181-1296.2025.v1.149.2.3394 |
| Harvard | А. Б. Хасанов, and U. Yu. Juraeva (2025) ‘INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(1), 93-101. https://doi.org/10.59251/2181-1296.2025.v1.149.2.3394 |
| BibTeX | @article{article2025,
title = {INTEGRAL REPRESENTATION FOR POLYHARMONIC FUNCTIONS IN TWO DIMENSIONAL EUCLIDEAN SPACE},
author = {А. Б. Хасанов and U. Yu. Juraeva},
journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
year = {2025},
volume = {1},
number = {1},
pages = {93-101},
doi = {10.59251/2181-1296.2025.v1.149.2.3394},
url = {https://doi.org/10.59251/2181-1296.2025.v1.149.2.3394}
} |
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