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If u solves ∇2u = 0, in D ⊆ Rn then,
(Here ∂D denotes the boundary of D and D̅ = D ∪ ∂D)

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  4. u is constant in D

Answer (Detailed Solution Below)

Option 2 :

Detailed Solution

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Concept:

If u is a harmonic function on a bounded domain D in Rn, then u attains its maximum value on the boundary of D.

Maximum principle:

 

 

Analysis:

∵ u solves ∇2 u = 0

∴ u is a harmonic function.

Hence, u will satisfy the maximum principle theorem and

 

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