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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Critical points of harmonic functions on domains in $ {\bf R}\sp{3}$


Author: Robert Shelton
Journal: Trans. Amer. Math. Soc. 261 (1980), 137-158
MSC: Primary 58E05; Secondary 49F05
DOI: https://doi.org/10.1090/S0002-9947-1980-0576868-7
MathSciNet review: 576868
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Abstract: It is shown that the critical point relations of Morse theory, together with the maximum principle, comprise a complete set of critical point relations for harmonic functions of three variables. The proof proceeds by first constructing a simplified example and then developing techniques to modify this example to realize all admissible possibilities. Techniques used differ substantially from those used by Morse in his solution of the analogous two-variable problem.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0576868-7
Article copyright: © Copyright 1980 American Mathematical Society