Boundary properties of minimal harmonic functions
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- by John T. Kemper
- Proc. Amer. Math. Soc. 60 (1976), 193-196
- DOI: https://doi.org/10.1090/S0002-9939-1976-0486579-9
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Abstract:
Certain elements of the boundary dependence of minimal harmonic functions in Euclidean domains are considered. For a given minimal harmonic function h on a domain $\Omega$, sets on the boundary of $\Omega$ or (relative) neighborhoods of such sets are sought wherein the behavior of h determines h in all of $\Omega$. The set of determining singletons on the boundary is shown to be connected.References
- Marcel Brelot, Le problème de Dirichlet. Axiomatique et frontière de Martin, J. Math. Pures Appl. (9) 35 (1956), 297–335 (French). MR 100173
- Marcel Brelot, On topologies and boundaries in potential theory, Lecture Notes in Mathematics, Vol. 175, Springer-Verlag, Berlin-New York, 1971. Enlarged edition of a course of lectures delivered in 1966. MR 0281940
- Richard A. Hunt and Richard L. Wheeden, Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc. 147 (1970), 507–527. MR 274787, DOI 10.1090/S0002-9947-1970-0274787-0
- Robert S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137–172. MR 3919, DOI 10.1090/S0002-9947-1941-0003919-6
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 193-196
- MSC: Primary 31B25
- DOI: https://doi.org/10.1090/S0002-9939-1976-0486579-9
- MathSciNet review: 0486579