Notice that the function xy is harmonic in the half-plane

Chapter 7, Problem 5

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QUESTION:

Notice that the function  is harmonic in the half-plane  and vanishes on the boundary line . The function  has the same properties. Does this mean that the solution is not unique? Explain.

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QUESTION:

Notice that the function  is harmonic in the half-plane  and vanishes on the boundary line . The function  has the same properties. Does this mean that the solution is not unique? Explain.

ANSWER:

Step 1 of 4

Given: the function  is harmonic in the half-plane  and vanishes on the boundary line . The function  has the same properties.

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