O‘zbekiston matematika jurnali Ҷилди 69 № 3 (2025) · Саҳифаҳои 168-175
The Dirichlet problem in the class of m-convex functions
Sharipov Rasulbek Axmedovich
Аннотатсия
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.
strongly m-subharmonic functions, m-convex functions, Borel measures, Hessians, Dirichlet problem
Манбаи метамаълумот: бойгонии OAI-PMH-и маҷалла · Sindex матни пурраро нигоҳ намедорад, ба манбаъ пайванд медиҳад.