Nagoya Mathematical Journal

The $P$-harmonic boundary and energy-finite solutions of $\Delta u=Pu$

Y. K. Kwon, L. Sario, and J. Schiff

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 42 (1971), 31-41.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118798297

Mathematical Reviews number (MathSciNet)
MR0288696

Zentralblatt MATH identifier
0192.45404

Subjects
Primary: 53.72
Secondary: 30.00

Citation

Kwon, Y. K.; Sario, L.; Schiff, J. The $P$-harmonic boundary and energy-finite solutions of $\Delta u=Pu$. Nagoya Math. J. 42 (1971), 31--41. https://projecteuclid.org/euclid.nmj/1118798297


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References

  • [1] M. Glasner-R. Katz, On thebehavior of solutions of uPu at theRoyden boundary, J. Analyse Math. 22 (1969), 343-354.
  • [2] Y.K. Kwon-L. Sario, A maximum principlefor bounded harmonicfunctions on Riemannian spaces, Canad. J. Math. 22(1970), 847-854.
  • [3] Harmonic functions on a subregion of a Riemannian manifold, J. Ind. Math. Soc. (to appear).
  • [4] Harmonic functions on a subregion of a Riemannian manifold, TheP-singular point of theY-compactification for uPu, Bull. Amer. Math. Soc. (to appear).
  • [5] Y.K. Kwon-L. Sario-J. Scruff, Bounded energy-finite solutions of uPu on aRiemannian manifold, Nagoya. Math. J. (to appear).
  • [6] M. Nakai, A measure on the harmonic boundary of a Riemann surface,Nagoya Math. J. 17 (1960), 181-218.
  • [7] M. Nakai-L. Sario, A newoperatorfor ellipticequations andtheP-compactification for ii–Pu, Math. Ann. 189(1970), 242-256.
  • [8] H.L. Royden, The equationu– Pu and the classification of open Riemann surfaces,Ann Acad. Sci. Fenn. Ser. A.I. 271 (1959), 27 pp.
  • [9] L. Sario-M. Nakai, Classification theory of Riemannsurfaces, Springer, 1970, 446 pp. Universityof California, Los Angeles