Seminars: R. A. Sharipov, Maximal $m$-convex functions and the Dirichlet problem in the class of $m$-convex functions

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) April 17, 2025 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Maximal $m$-convex functions and the Dirichlet problem in the class of $m$-convex functions R. A. Sharipov Urgench State University named after Al-Khorezmi
Abstract: In this talk we consider one of the key concepts of potential theory — extremal (maximal) $m$-convex functions and the related Dirichlet problem. The formulation and solvability of the Dirichlet problem in non-strictly $m$-convex domains are studied, and conditions for the existence of a solution are found. The concept of Hessians in the class of bounded $m$-convex functions is introduced, which are considered as Borel measures. It is shown that the corresponding measures for maximal $m$-convex functions are trivial. Website: https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09