Extreme nonmonotoneity of the Picard principle

DOI10.1007/BF01458434zbMath0627.31002OpenAlexW1975073182MaRDI QIDQ1092283

Mitsuru Nakai, Toshimasa Tada

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164419

zbMATH Keywords

extreme pointsdensityconvex setPicard principlenonnegative locally Hölder continuous functionPicard dimension

Mathematics Subject Classification ID

Ideal boundary theory for Riemann surfaces (30F25) Martin boundary theory (31C35) Integral representations, integral operators, integral equations methods in two dimensions (31A10) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (7)

Martin boundary for Schrödinger operators with singularity ⋮ Picard dimension of signed radial Kato measures ⋮ Strong nonmontonicity of the picard dimension ⋮ Nonmonotoneity of Picard principle for Schrödinger operators ⋮ Monotonicity of non-Liouville property for positive solutions of skew product elliptic equations ⋮ On construction of Martin boundaries for second order elliptic equations ⋮ Essential sets of Picard principle for rotation free densities

Cites Work

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• Harmonic spaces and their potential theory
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• The space of non-negative solutions of the equation $\Delta u=pu$ on a Riemann surface
• Harmonic and relative harmonic dimensions
• Nonmonotoneity of Picard Principle
• Picard principle for finite densities
• Minimal Positive Harmonic Functions

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