No abstract uploaded!

We show that interpolation to a function, analytic on a compact set$E$in the complex plane, can yield maximal convergence only if a subsequence of the interpolation points converges to the equilibrium distribution on$E$in the weak sense. Furthermore, we will derive a converse theorem for the case when the measure associated with the interpolation points converges to a measure on$E$, which may be different from the equilibrium measure.

No abstract uploaded!

We construct singular solutions to equations $$div\mathcal{A}(x,\nabla u) = 0,$$ similar to the$p$-Laplacian, that tend to ∞ on a given closed set of$p$-capacity zero. Moreover, we show that every$G$_{δ}-set of vanishing$p$-capacity is the infinity set of some$A$-superharmonic function.

Let Ω be a bounded convex domain in C_{$n$}, with smooth boundary of finite type$m$.