On harmonic continuation
Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 54-56

Voir la notice de l'article provenant de la source Cambridge University Press

Let D be a bounded, closed, simply-connected domain whose boundary C consists of a finite number of analytic Jordan curves. Let γ be any analytic arc of C. Then we shall prove the following theorem.Theorem 1. Let u(x, y) be harmonic in the interior of D and continuous on γ, and let ρu(x, y)/ρn=g(s) when (x, y) is on γ, where g(s) is an analytic function of arc-length s along γ. Then u(x, y) can be harmonically continued across γ.
Eastham, M. S. P. On harmonic continuation. Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 54-56. doi: 10.1017/S2040618500034717
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[1] 1.Ahlfors, L. V., Complex analysis (New York, 1953). Google Scholar

[2] 2.Nehari, Z., Conformal mapping (New York, 1952). Google Scholar

[3] 3.Sternberg, W. J. and Smith, T. L., The theory of potential andspherical harmonics (Toronto, 1946). Google Scholar

[4] 4.Ugaeri, T., On the harmonic prolongation, J. Math. Soc. Japan 1 (1949), 262–5. Google Scholar | DOI

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