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Timeline for Extension of harmonic function

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Jul 6, 2012 at 23:49 comment added Slm2004 Yes. If the boundary behavior of u at this smooth portion is not nice enough, of course we can not extend it. What if I add assumption that $\frac{\partial u}{\partial v}$ exists on this portion?
Jul 6, 2012 at 23:44 vote accept Slm2004
Jul 6, 2012 at 17:06 comment added Pietro Majer I understood the question as: is there a harmonic extension of $u$ on a strictly larger domain $\Omega'$. Or maybe you want a continuous extension to $\Omega'$ which is harmonic on $\Omega'\setminus\partial \Omega$?
Jul 6, 2012 at 16:59 history answered Pietro Majer CC BY-SA 3.0