ArticleOriginal scientific text
Title
Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions
Authors 1
Affiliations
- Department of Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
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.
Bibliography
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- S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992.
- C B. R. Choe, Bôcher's theorem for M-harmonic functions, Houston J. Math. 18 (1992), 539-549.
- 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).
- 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).
- R. Harvey and J. C. Polking, A Laurent expansion for solutions to elliptic equations, Trans. Amer. Math. Soc. 180 (1973), 407-413.
- N E. Nelson, A proof of Liouville's theorem, Proc. Amer. Math. Soc. 12 (1961), 995.
- W M. Wachman, Generalized Laurent series for singular solutions of elliptic partial differential equations, Proc. Amer. Math. Soc. 15 (1964), 101-108.
Pages:
257-265
Main language of publication
English
Received
1997-05-15
Published
1998
Exact and natural sciences