Elementary proofs of the Liouville and Bôcher theorems for polyharmonic functions

• Autorzy: Ewa Ligocka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 31B30: Biharmonic and polyharmonic equations and functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 3
• Strony: 257-265

Daty

wydano

1998

otrzymano

1997-05-15

Twórcy

autor

Ewa Ligocka

• 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.