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Wiener's type regularity criteria on the complex plane

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Siciak J.

Annales Polonici Mathematici

1997

tom 66

nr 1

203-221

We present a number of Wiener's type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that $d(t^{-1}E ∩ {|z-a| ≤ 1}) ≥ const > 0$ for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ \ E with pole at infinity is Hölder continuous.

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1 Annales Polonici Mathematici

1 Siciak J.

1 1997

Wyniki wyszukiwania

Wiener's type regularity criteria on the complex plane