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The boundary modulus of
continuity of harmonic functions
Elgin Harold Johnston |
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Vol. 90 (1980), No. 1, 87–98
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Abstract |
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Let G be a bounded domain in the complex plane and let u(z) be continuous on Ḡ. In this paper we study the boundary modules of continuity, ω(δ), of u on ∂G and the modulus of continuity, ω(δ), of u on Ḡ. We investigate the extent to which the inequality “ω(δ) ≤ω(δ)” holds when u is harmonic on G and show that the precise formulation of such inequalities depends on the smoothness of ∂G. |
Mathematical Subject Classification 2000
Primary: 31A05
Secondary: 30A10
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Milestones
Received: 2 June 1978
Published: 1 September 1980
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Authors |
| Elgin Harold Johnston | |
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