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Dirichlet integral and Picard principle
Published online by Cambridge University Press: 22 January 2016
Extract
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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1982
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