Harmonic function and Lipschitz domain

Sidi

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Joined
May 4, 2012
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2
Hello, I really need help with this claim:

If u is harmonic function on connected Lipschitz domain D in R3 vanishing continuously on an open set V contained in the boundary of D and whose normal derivative vanishes on a subset of V with positive surface measure, then u is identically zero on D.

Is it true or not? Note that the domain is Lipschitz , neither C1,1 nor convex.

Thank you so much for your reply !!!
 
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