Geodesic
Uniform Harmonic Approximation with Continuous Extension to the Boundary
Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1375-1388

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

Let G be a domain in the complex plane and F a nonempty subset of G such that F is the closure in G of its interior F 0. We will say f ∊ C 1(F) if f is continuous on F and possesses continuous first partial derivatives in F which extend continuously to F as finite-valued functions. Let G* – F be connected and locally connected, f ∊ C 1(F) be harmonic in F 0, and E be a subset of ∂F ∩ ∂G (here G* denotes the one-point compactification of G and the boundaries ∂F, ∂G are taken in the extended plane). Suppose there is a sequence 〈hn 〉 of functions harmonic in G such that uniformly on F as n → ∞. 
Goldstein, M.; Ow, W. H. Uniform Harmonic Approximation with Continuous Extension to the Boundary. Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1375-1388. doi: 10.4153/CJM-1988-061-3
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