Local and global Hölder regularity of compact set

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.