O‘zbekiston matematika jurnali 69-jild 3-son (2025) · 168-175-betlar
The Dirichlet problem in the class of m-convex functions
Sharipov Rasulbek Axmedovich
Annotatsiya
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
Metadata manbasi: jurnal OAI-PMH arxivi · Sindex toʻliq matnni saqlamaydi, manbaga havola beradi.