Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 46, 1-48
- https://doi.org/10.1017/s0027763000014756
Abstract
Consider a relatively compact region Ω of a Riemann surface R. The term Dirichlet integral over Ω, DΩ(·), is used for the variation whose Euler-Lagrange equation is Δu = 0 on Ω and the term energy integral over Ω, , is used for the variation with Euler-Lagrange equationKeywords
This publication has 12 references indexed in Scilit:
- Dirichlet mappings of Riemannian manifolds and the equation Δu = PuJournal of Differential Equations, 1971
- Dirichlet finite solutions of $\Delta u=Pu$ on open Riemann surfacesKodai Mathematical Journal, 1971
- Dirichlet finite solutions of Δ𝑢=𝑃𝑢, and classification of Riemann surfacesBulletin of the American Mathematical Society, 1971
- Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinusAnnales de l'institut Fourier, 1969
- Quelques propriétés des sursolutions et sursolutions locales d'une équation uniformément elliptique de la forme $Lu=-sum_i{partialoverpartial x_i}(sum_j a_{ij}{partial uoverpartial x_j})=0$Annales de l'institut Fourier, 1966
- An axiomatic treatment of pairs of elliptic differential equationsAnnales de l'institut Fourier, 1966
- The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of BrelotAnnales de l'institut Fourier, 1965
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinusAnnales de l'institut Fourier, 1965
- On Harnack's theorem for elliptic differential equationsCommunications on Pure and Applied Mathematics, 1961
- The space of bounded solutions of the equation $\Delta u = pu$ on a Riemann surfaceProceedings of the Japan Academy, Series A, Mathematical Sciences, 1960