Critical points of harmonic functions on domains in $\textbf {R}^{3}$
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- by Robert Shelton PDF
- Trans. Amer. Math. Soc. 261 (1980), 137-158 Request permission
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.References
- Marston Morse, Topological Methods in the Theory of Functions of a Complex Variable, Annals of Mathematics Studies, No. 15, Princeton University Press, Princeton, N. J., 1947. MR 0021089
- Marston Morse, Equilibrium points of harmonic potentials, J. Analyse Math. 23 (1970), 281–296. MR 277737, DOI 10.1007/BF02795505
- Marston Morse and Stewart S. Cairns, Critical point theory in global analysis and differential topology: An introduction, Pure and Applied Mathematics, Vol. 33, Academic Press, New York-London, 1969. MR 0245046
Additional Information
- © Copyright 1980 American Mathematical Society
- 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