An example concerning Sadullaev's boundary relative extremal functions

We exhibit a smoothly bounded domain $\mathrm{\Omega }$ with the property that for suitable $K\subset \mathrm{\partial }\mathrm{\Omega }$ and $z\in \mathrm{\Omega }$ the “Sadullaev boundary relative extremal functions” satisfy the inequality ${\omega }_1(z,K,\mathrm{\Omega })<{\omega }_2(z,K,\mathrm{\Omega })\le \omega (z,K,\mathrm{\Omega })$.