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 |
| Nashr sanasi | 2025-09-05 |
| Jild | 69 |
| Son | 3 |
| Betlar | 168-175 |
| DOI | 10.29229/uzmj.2025-3-18 |
DOI: 10.29229/uzmj.2025-3-18 · Maqolaning asl sahifasi
strongly m-subharmonic functions, m-convex functions, Borel measures, Hessians, Dirichlet problem
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