An example concerning Sadullaev's boundary relative extremal functions

Abstract

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

3 pages