On the behavior of solutions of \(\Delta u = Pu\) at the Royden boundary

DOI10.1007/BF02786798zbMath0179.15201OpenAlexW1973753152MaRDI QIDQ2534359

Yanyan Li

Publication date: 1969

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02786798

zbMATH Keywords

partial differential equations

Related Items (21)

A note on the Royden boundary ⋮ The P-Harmonic Boundary and Energy-Finite Solutions of Δu = Pu ⋮ Bounded Energy-Finite Solutions of Δu = Pu on a Riemannian Manifold ⋮ The 𝑃-singular point of the 𝑃-compactification for Δ𝑢=𝑝𝑢 ⋮ A remark on classification of Riemannian manifolds with respect to Δ𝑢=𝑃𝑢 ⋮ Relations between boundaries of a riemannian manifold ⋮ Dirichlet finite solutions of Δ𝑢=𝑃𝑢, and classification of Riemann surfaces ⋮ Minimality in families of solutions of $\Delta u = Pu$ on Riemannian manifolds ⋮ Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfaces ⋮ Minimality in families of solutions of $\Delta u=Pu$ on Riemann surfaces ⋮ The roles of sets of nondensity points ⋮ Images of reduction operators ⋮ Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions ⋮ Integration near the Royden boundary of a Riemannian manifold ⋮ Integration near the Royden boundary of a Riemannian manifold ⋮ Examples in the classification theory of Riemannian manifolds and the equation \(\Delta u=Pu\) ⋮ 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 \(P\geq 0\). ⋮ Dirichlet mappings of Riemannian manifolds and the equation \(\Delta u = Pu\). ⋮ Dirichlet finite biharmonic functions with Dirichlet finite Laplacians ⋮ Surjective extension of the reduction operator

Cites Work

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• Function-theoretic degeneracy criteria for Riemannian manifolds
• An axiomatic treatment of pairs of elliptic differential equations
• The Royden boun dry of a Riemannian manifold
• Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann
• On a Ring Isomorphism Induced by Quasiconformal Mappings
• A set of capacity zero and the equation $\Delta u=Pu$
• The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface
• A Measure on the Harmonic Boundary of a Riemann Surface
• The space of bounded solutions of the equation $\Delta u = pu$ on a Riemann surface
• A Minimal Compactification for Extending Continuous Functions
• Classification of Riemann surfaces

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