Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
257-265
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-05-15
Twórcy
autor
- Department of Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
- [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.
- [3] C B. R. Choe, Bôcher's theorem for M-harmonic functions, Houston J. Math. 18 (1992), 539-549.
- [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.
- [7] N E. Nelson, A proof of Liouville's theorem, Proc. Amer. Math. Soc. 12 (1961), 995.
- [8] W M. Wachman, Generalized Laurent series for singular solutions of elliptic partial differential equations, Proc. Amer. Math. Soc. 15 (1964), 101-108.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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