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Dirichlet integral and Picard principle

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai  and
Toshimasa Tada
Mitsuru Nakai
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466, Japan
Toshimasa Tada
Affiliation:
Department of Mathematics, Daido Institute of Technology, Doido, Minami, Nagoya 457, Japan
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A density P on the punctured unit disk Ω:0 < |z| <1 is a 2-form P(z)dxdy whose coefficient P(z) is a real valued nonnegative locally Hölder continuous function on the closed punctured unit disk Ω:0< |z| <≦1. Here we consider Ω as an end of the punctured sphere 0 < |z| ≦ + + so that the point z = 0 is viewed as the ideal boundary δΣ of Σ and the unit circle |z| = 1 as the relative boundary δΣ of Σ. We denote by D = D(Σ) the family of densities on Σ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 86 , June 1982 , pp. 85 - 99
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

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