Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions

Ewa Ligocka

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 3, page 257-265
  • ISSN: 0066-2216

Abstract

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Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions are given. These proofs are on the calculus level and use only the basic knowledge of harmonic functions given in Axler, Bourdon and Ramey's book.

How to cite

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Ewa Ligocka. "Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions." Annales Polonici Mathematici 68.3 (1998): 257-265. <http://eudml.org/doc/270330>.

@article{EwaLigocka1998,
abstract = {Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions are given. These proofs are on the calculus level and use only the basic knowledge of harmonic functions given in Axler, Bourdon and Ramey's book.},
author = {Ewa Ligocka},
journal = {Annales Polonici Mathematici},
keywords = {polyharmonic function; Liouville theorem; polyharmonic Bôcher theorem; elementary proofs},
language = {eng},
number = {3},
pages = {257-265},
title = {Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions},
url = {http://eudml.org/doc/270330},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Ewa Ligocka
TI - Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 3
SP - 257
EP - 265
AB - Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions are given. These proofs are on the calculus level and use only the basic knowledge of harmonic functions given in Axler, Bourdon and Ramey's book.
LA - eng
KW - polyharmonic function; Liouville theorem; polyharmonic Bôcher theorem; elementary proofs
UR - http://eudml.org/doc/270330
ER -

References

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  1. [1] N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1983. 
  2. [2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992. Zbl0765.31001
  3. [3] C B. R. Choe, Bôcher's theorem for M-harmonic functions, Houston J. Math. 18 (1992), 539-549. Zbl0787.31007
  4. [4] S. D. Eĭdel'man and T. G. Pletneva, Bôcher's theorem for positive solutions of elliptic equations of arbitrary order, Mat. Issled. 8 (1973), 173-177, 185 (in Russian). 
  5. [5] F A. I. Firdman, The generalized Bôcher theorem for positive solutions of quasielliptic equations, Voronezh. Gos. Univ. Trudy Mat. Fak. Publ. 1973, 111-121; Ref. Zh. Mat. 1974 7B 331 (in Russian). 
  6. [6] R. Harvey and J. C. Polking, A Laurent expansion for solutions to elliptic equations, Trans. Amer. Math. Soc. 180 (1973), 407-413. Zbl0285.35024
  7. [7] N E. Nelson, A proof of Liouville's theorem, Proc. Amer. Math. Soc. 12 (1961), 995. Zbl0124.31203
  8. [8] W M. Wachman, Generalized Laurent series for singular solutions of elliptic partial differential equations, Proc. Amer. Math. Soc. 15 (1964), 101-108. Zbl0145.14503

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