We give a very simple function theoretic proof to a Liouville type theorem for harmonic functions defined on exterior domains obtained and proved in a convexity theoretic method by F. Cammaroto and A. Chinnı. The theorem itself is also slightly generalized.
✦ LIBER ✦
A Liouville-Type Theorem for Harmonic Functions on Exterior Domains
✍ Scribed by F. Cammaroto; A. Chinnı̀
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 84 KB
- Volume
- 244
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
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We prove that any finitely connected domain in the plane can be distorted so that it becomes ''graviequivalent'' to a signed measure with arbitrarily small support. Precisely: if D ; ރ is a bounded, finitely connected domain with analytic Ž . boundary then for any a g D and r ) 0, ) 0 with B a, r