Seminars: Sh. Ya. Khursanov, Local and global Hölder regularity of compact set

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) May 4, 2017 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Local and global Hölder regularity of compact set Sh. Ya. Khursanov National University of Uzbekistan named after M. Ulugbek, Tashkent
Abstract: For compact set $K\subset {{\mathbb{C}}^{n}}$ we define Green function $V(x,K)=\sup \{u(x):u\in sh({{\mathbb{R}}^{n}}),{{\left. u \right\|}_{K}}\le -1,~{{\left. u \right\|}_{{{\mathbb{R}}^{n}}}}\le 0\}$. If ${{x}_{0}}\in \partial K$ is Hölder barer boundary point of $K$, then Green function $V(x,K)$ is locally Hölder regular iff the point ${{x}_{0}}$ is globally Hölder regular.