Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral

DOI10.1017/S0027763000014756zbMath0212.45002OpenAlexW1559640537WikidataQ115336427 ScholiaQ115336427MaRDI QIDQ5614193

Moses Glasner, Mitsuru Nakai

Publication date: 1972

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

Full work available at URL: https://doi.org/10.1017/s0027763000014756

Mathematics Subject Classification ID

Dirichlet forms (31C25) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (3)

Liouville theorems for \(f\)-harmonic maps into Hadamard spaces ⋮ Harmonic boundaries of Riemannian manifolds ⋮ Images of reduction operators

Cites Work

• The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot
• Quelques propriétés des sursolutions et sursolutions locales d'une équation uniformement elliptique de la forme \(Lu =-\sum_ i {\partial\over\partial x_ i} \left(\sum_ j \alpha_{ij} {\partial u\over\partial x_ j}\right) =0\)
• An axiomatic treatment of pairs of elliptic differential equations
• Dirichlet mappings of Riemannian manifolds 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
• On Harnack's theorem for elliptic differential equations
• Dirichlet finite solutions of Δ𝑢=𝑃𝑢, and classification of Riemann surfaces
• Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfaces

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