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A maximum principle for $ n$-metaharmonic functions

Authors: Shui Nee Chow and D. R. Dunninger
Journal: Proc. Amer. Math. Soc. 43 (1974), 79-83
MSC: Primary 35J30
MathSciNet review: 0330753
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Abstract: A class of $ n$-metaharmonic functions is shown to satisfy the inequality, $ \vert u(x)\vert \leqq k\vert u({x_0})\vert$, where $ x$ is an arbitrary point in a domain $ \bar D,{x_0}$ is some fixed point on the boundary of $ D$, and $ k$ is a constant.

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  • [1] I. N. Vekua, New methods for solving elliptic equations, OGIZ, Moscow, 1948; English transl., Series in Appl. Math., vol. 1, North-Holland, Amsterdam; Interscience, New York, 1967. MR 11, 598; 35 #3243. MR 0034503 (11:598a)
  • [2] J. L. Massera, Contributions to stability theory, Ann. of Math. (2) 64 (1956), 182-206. MR 18, 42. MR 0079179 (18:42d)
  • [3] D. R. Dunninger, Maximum principles for solutions of some fourth order elliptic equations, J. Math. Anal. Appl. 37 (1972), 655-658. MR 0312040 (47:602)

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Keywords: $ n$-metaharmonic functions, maximum principle, Liapunov stability theory
Article copyright: © Copyright 1974 American Mathematical Society

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