- Tytuł:
- Wieners type regularity criteria on the complex plane
- Autorzy:
- Siciak, Józef
- Powiązania:
- https://bibliotekanauki.pl/articles/1294812.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
subharmonic functions
logarithmic potential theory
Green function
regular points
Hölder Continuity Property - Opis:
- 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.
- Źródło:
-
Annales Polonici Mathematici; 1997, 66, 1; 203-221
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł