# Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions

Annales Polonici Mathematici (1998)

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

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topEwa 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

top- [1] N. Aronszajn, T. Creese and L. Lipkin, Polyharmonic Functions, Clarendon Press, Oxford, 1983.
- [2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992. Zbl0765.31001
- [3] C B. R. Choe, Bôcher's theorem for M-harmonic functions, Houston J. Math. 18 (1992), 539-549. Zbl0787.31007
- [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] 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] 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] N E. Nelson, A proof of Liouville's theorem, Proc. Amer. Math. Soc. 12 (1961), 995. Zbl0124.31203
- [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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