×

The equation \(\Delta u=Pu\) on \(E^m\) with almost rotation free \(P\geq O\). (English) Zbl 0226.31006


MSC:

31C12 Potential theory on Riemannian manifolds and other spaces
31A35 Connections of harmonic functions with differential equations in two dimensions
31B35 Connections of harmonic functions with differential equations in higher dimensions
34B27 Green’s functions for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. GIASNER-R. KATZ, On the behavior of solutions of u = Pu at the Royden boundary, J. Di Analyse Math., 22(1969), 345-354. · Zbl 0179.15201
[2] M. GiASNER -R. KATZ -M. NAKAI, Examples in the classification theory of Riemannia manifolds and the equation u = Pu, Math. Z., 121(1971), 233-238. · Zbl 0213.12305
[3] S. ITO, Fundamental solutions of parabolic differential equations and boundaryvalu problems, Japan. J. Math., 27(1957), 55-102. · Zbl 0092.31101
[4] F-Y. MAEDA, Boundary value problems for the equation u-pu –0 with respect to a ideal boundary, J. Sci. Hiroshima univ., 32(1968), 85-146. · Zbl 0157.42901
[5] C. MIRANDA, Partial Differential Equations of Elliptic Type, Springer, 1970 · Zbl 0198.14101
[6] L. MYRBERG, Uher die Existenz der Greenschen Funktion der Gleichung u = c(P*)u au Riemannschen Flachen, Ann. Acad. Sci. Fenn., 170(1954). · Zbl 0055.07303
[7] M. NAKAI, The space of bounded solutions of the equation u = Pu on a Rieman surface, Proc. Japan Acad., 36(1960), 267-272. · Zbl 0102.29805
[8] M. NAKAI, Dirichlet finite solutions of u = Pu, and classification of Riemann surfaces, Bull. Amer. Math. Soc., 77(1971), 381-385. THE EQUATION u = Pu ON ETM431 · Zbl 0223.30010
[9] M. NAKAI, Dirichlet finite solutions of # = Pu on open Riemann surfaces, Kdai Math Sem. Rep. (to appear). · Zbl 0226.31004
[10] M. OZAWA, Classification of Riemann surfaces, Kdai Math. Sem. Rep., 4(1952), 63-76 · Zbl 0048.31803
[11] H. L. ROYDEN, The eqation M = Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn., 271(1959). · Zbl 0096.05803
[12] L. SARIO-M. NAKAI, Classification Theory of Riemann Surfaces, Springer, 1970 · Zbl 0199.40603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.