Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfaces

DOI10.2996/kmj/1138846412zbMath0226.31004OpenAlexW2065779697MaRDI QIDQ5632889

Mitsuru Nakai

Publication date: 1971

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138846412

Mathematics Subject Classification ID

Dirichlet forms (31C25) Classification theory of Riemann surfaces (30F20) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (13)

Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral ⋮ A remark on classification of Riemannian manifolds with respect to Δ𝑢=𝑃𝑢 ⋮ Order Comparisons on Canonical Isomorphisms ⋮ A remark on classification of Riemann surfaces with respect to Δ𝑢=𝑃𝑢 ⋮ Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral ⋮ Canonical isomorphisms of energy finite solutions of Δu = Pu on open Riemann surfaces ⋮ Uniform densities on hyperbolic Riemannl surfaces ⋮ Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions ⋮ Densities without unbounded positive solutions ⋮ An example on canonical isomorphism ⋮ The equation \(\Delta u=Pu\) on \(E^m\) with almost rotation free \(P\geq O\). ⋮ The equation \(\Delta u=Pu\) on the unit disk with almost rotation free \(P\geq 0\). ⋮ Surjective extension of the reduction operator

Cites Work

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• On the behavior of solutions of \(\Delta u = Pu\) at the Royden boundary
• Examples in the classification theory of Riemannian manifolds and the equation \(\Delta u=Pu\)
• The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface
• The space of bounded solutions of the equation $\Delta u = pu$ on a Riemann surface
• Dirichlet finite solutions of Δ𝑢=𝑃𝑢, and classification of Riemann surfaces
• Classification of Riemann surfaces

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