The equation \(\Delta u=Pu\) on \(E^m\) with almost rotation free \(P\geq O\).

DOI10.2748/tmj/1178242591zbMath0226.31006OpenAlexW1982756635MaRDI QIDQ2549078

Mitsuru Nakai

Publication date: 1971

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178242591

Mathematics Subject Classification ID

Green's functions for ordinary differential equations (34B27) Connections of harmonic functions with differential equations in higher dimensions (31B35) Potential theory on Riemannian manifolds and other spaces (31C12) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (5)

A remark on classification of Riemannian manifolds with respect to Δ𝑢=𝑃𝑢 ⋮ Order Comparisons on Canonical Isomorphisms ⋮ Images of reduction operators ⋮ Uniform densities on hyperbolic Riemannl surfaces ⋮ The equation \(\Delta u=Pu\) on the unit disk with almost rotation free \(P\geq 0\).

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 \(\Delta u=Pu\)
• Fundamental solutions of parabolic differential equations and boundary value problems
• 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
• Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfaces
• Classification of Riemann surfaces

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