The well-known classical Dirichlet problem states that if $D\subset {\mathbb R}^{n}$ is a regular domain, then for any continuous function $\varphi (\xi )\in C(\partial D)$, there exists a unique harmonic function $\omega (x)\in C(\overline{D})$, such that $\omega |_{\partial D} =\varphi $. In the work of Sadullaev-Sharipov, under an additional condition of strict $m$-convexity of the domain $D\subset {\mathbb R}^{n} $, an analogous result for $m$-convex $(m-cv)$ functions has been proven.
| Mualliflar | Sharipov Rasulbek Axmedovich |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-05 |
| Jild | 69 |
| Son | 3 |
| Betlar | 168-175 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-18 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-18 · Maqolaning asl sahifasi
strongly m-subharmonic functions, m-convex functions, Borel measures, Hessians, Dirichlet problem
| APA | Sharipov Rasulbek Axmedovich (2025). The Dirichlet problem in the class of m-convex functions. O‘zbekiston matematika jurnali, 69(3), 168-175. https://doi.org/10.29229/uzmj.2025-3-18 |
|---|---|
| GOST (OAK) | Sharipov Rasulbek Axmedovich The Dirichlet problem in the class of m-convex functions // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 168-175. – DOI: 10.29229/uzmj.2025-3-18. |
| MLA | Sharipov Rasulbek Axmedovich. “The Dirichlet problem in the class of m-convex functions.” O‘zbekiston matematika jurnali, 69(3), 168-175, 2025. https://doi.org/10.29229/uzmj.2025-3-18 |
| Chicago | Sharipov Rasulbek Axmedovich. “The Dirichlet problem in the class of m-convex functions.” O‘zbekiston matematika jurnali, 69(3), 168-175 (2025). https://doi.org/10.29229/uzmj.2025-3-18 |
| Harvard | Sharipov Rasulbek Axmedovich (2025) ‘The Dirichlet problem in the class of m-convex functions’, O‘zbekiston matematika jurnali, 69(3), 168-175. https://doi.org/10.29229/uzmj.2025-3-18 |
| BibTeX | @article{sharipovrasulbekaxmedovich2025,
title = {The Dirichlet problem in the class of m-convex functions},
author = {Sharipov Rasulbek Axmedovich},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {168-175},
doi = {10.29229/uzmj.2025-3-18},
url = {https://doi.org/10.29229/uzmj.2025-3-18}
} |
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