O‘zbekiston matematika jurnali Volume 69 Issue 3 (2025) · pp. 168-175
The Dirichlet problem in the class of m-convex functions
Sharipov Rasulbek Axmedovich
Abstract
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
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