The solution to the Dirichlet Problem in a disc should give an extension to arbitrarily large discs centred at the origin, with radius less than 1.
2026-03-29 05:11:29.1774761089
Does any harmonic function on the punctured disc have an extension to the entire unit disc?
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No, for example $\ln |x|$ in $\mathbb R^2\setminus \{ 0\}.$